Quiz 4 Discrete distributions
1. A new car salesperson knows that he sells cars to one in every twenty customers
who enter the showroom. What is the probability that he will sell a new car to exactly
two of the next three customers?
*a. 0.007
b. 0.021
c. 0.003
d. 0.010
e. 0.001
2. A new car salesperson knows that he sells cars to one in every twenty customers
who enter the showroom. What is the probability that he will sell a new car to exactly
two of the next five customers?
a. 0.007
*b. 0.021
c. 0.003
d. 0.010
e. 0.001
3. A new car salesperson knows that he sells cars to one in every thirty customers who
enter the showroom. What is the probability that he will sell a new car to exactly two
of the next three customers?
a. 0.007
b. 0.021
*c. 0.003
d. 0.010
e. 0.001
4. A new car salesperson knows that he sells cars to one in every thirty customers who
enter the showroom. What is the probability that he will sell a new car to exactly two
of the next five customers?
a. 0.007
b. 0.021
c. 0.003
*d. 0.010
e. 0.001
5. A new car salesperson knows that he sells cars to one in every twenty customers
who enter the showroom. What is the probability that he will sell a new car to exactly
three of the next five customers?
a. 0.007
b. 0.021
c. 0.003
d. 0.010
*e. 0.001
6. Approximately 84% of persons living in Cape Town who are aged 70 to 84 live in
elderly care facilities. If four persons are randomly selected from this population,
what is the probability that exactly two of the four live in elderly care facilities?
*a. 0.108
b. 0.244
c. 0.007
d. 0.319
e. 0.379
7. Approximately 72% of persons living in Cape Town who are aged 70 to 84 live in
elderly care facilities. If four persons are randomly selected from this population,
what is the probability that exactly two of the four live in elderly care facilities?
a. 0.108
*b. 0.244
c. 0.007
d. 0.319
e. 0.379
8. Approximately 84% of persons living in Cape Town who are aged 70 to 84 live in
elderly care facilities. If six persons are randomly selected from this population, what
is the probability that exactly two of the six live in elderly care facilities?
a. 0.108
b. 0.244
*c. 0.007
d. 0.319
e. 0.379
9. Approximately 64% of persons living in Cape Town who are aged 70 to 84 live in
elderly care facilities. If four persons are randomly selected from this population,
what is the probability that exactly two of the four live in elderly care facilities?
a. 0.108
b. 0.244
c. 0.007
*d. 0.319
e. 0.379
10. Approximately 84% of persons living in Cape Town who are aged 70 to 84 live in
elderly care facilities. If four persons are randomly selected from this population,
what is the probability that exactly three of the four live in elderly care facilities?
a. 0.108
b. 0.244
c. 0.007
d. 0.319
*e. 0.379
11. The listed occupations of stockholders of a national computer company included
9% who were housewives. If six of these stockholders are randomly selected, what is
the probability that none are housewives?
*a. 0.568
b. 0.011
c. 0.083
d. 0.282
e. 0.073
12. The listed occupations of stockholders of a national computer company included
9% who were housewives. If six of these stockholders are randomly selected, what is
the probability that exactly three are housewives?
a. 0.568
*b. 0.011
c. 0.083
d. 0.282
e. 0.073
13. The listed occupations of stockholders of a national computer company included
9% who were housewives. If six of these stockholders are randomly selected, what is
the probability that exactly two are housewives?
a. 0.568
b. 0.011
*c. 0.083
d. 0.282
e. 0.073
14. The listed occupations of stockholders of a national computer company included
19% who were housewives. If six of these stockholders are randomly selected, what
is the probability that none are housewives?
a. 0.568
b. 0.011
c. 0.083
*d. 0.282
e. 0.073
15. The listed occupations of stockholders of a national computer company included
19% who were housewives. If six of these stockholders are randomly selected, what
is the probability that exactly three are housewives?
a. 0.568
b. 0.011
c. 0.083
d. 0.282
*e. 0.073
16. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the probability that exactly ten out of the 120 CD players are defective?
*a. 0.040
b. 0.105
c. 0.163
d. 0.107
e. 0.063
17. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the probability that exactly 8 out of the 120 CD players are defective?
a. 0.040
*b. 0.105
c. 0.163
d. 0.107
e. 0.063
18. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the probability that exactly five out of the 120 CD players are defective?
a. 0.040
b. 0.105
*c. 0.163
d. 0.107
e. 0.063
19. A large manufacturing company that produces CD players believes that 1 out of
every 10 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the probability that exactly ten out of the 120 CD players are defective?
a. 0.040
b. 0.105
c. 0.163
*d. 0.107
e. 0.063
20. A large manufacturing company that produces CD players believes that 1 out of
every 10 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the probability that exactly 8 out of the 120 CD players are defective?
a. 0.040
b. 0.105
c. 0.163
d. 0.107
*e. 0.063
21. A study conducted at a certain university shows that 45% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that exactly 7 of them will have found a job in their chosen field?
*a. 0.201
b. 0.051
c. 0.078
d. 0.165
e. 0.140
22. A study conducted at a certain university shows that 45% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that exactly 10 of them will have found a job in their chosen field?
a. 0.201
*b. 0.051
c. 0.078
d. 0.165
e. 0.140
23. A study conducted at a certain university shows that 45% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that exactly 4 of them will have found a job in their chosen field?
a. 0.201
b. 0.051
*c. 0.078
d. 0.165
e. 0.140
24. A study conducted at a certain university shows that 55% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that exactly 7 of them will have found a job in their chosen field?
a. 0.201
b. 0.051
c. 0.078
*d. 0.165
e. 0.140
25. A study conducted at a certain university shows that 55% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that exactly 10 of them will have found a job in their chosen field?
a. 0.201
b. 0.051
c. 0.078
d. 0.165
*e. 0.140
26. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that exactly 7 of the 10
students got A’s for matric?
*a. 0.267
b. 0.233
c. 0.121
d. 0.250
e. 0.282
27. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that exactly 8 of the 10
students got A’s for matric?
a. 0.267
*b. 0.233
c. 0.121
d. 0.250
e. 0.282
28. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that exactly 9 of the 10
students got A’s for matric?
a. 0.267
b. 0.233
*c. 0.121
d. 0.250
e. 0.282
29. It is believed that 75% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that exactly 7 of the 10
students got A’s for matric?
a. 0.267
b. 0.233
c. 0.121
*d. 0.250
e. 0.282
30. It is believed that 75% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that exactly 8 of the 10
students got A’s for matric?
a. 0.267
b. 0.233
c. 0.121
d. 0.250
*e. 0.282
31. A manufacturing company has produced a new car seat for infants and it is
undergoing rigorous safety testing. The product will only be approved for usage if at
least 14 out of a sample of 15 seats meet the safety requirements. What is the
probability that the new product will be approved if each individual seat is three times
as likely to meet the safety requirements as not?
a. 0.976
b. 0.997
*c. 0.080
d. 0.003
e. 0.091
32. A recent survey in Cape Town revealed that 60% of the vehicles traveling on
highways, where speed limits are posted at 80 km per hour, were exceeding the limit.
Suppose you randomly record the speeds of 10 vehicles traveling on the N1 where the
speed limit is 80 km per hour. What is the probability that exactly ten vehicles are
exceeding the limit?
a. 0.01
*b. 0.006
c. 1
d. 0.00
e. 0.99
33. To harvest all the wheat from a field requires 5 sunny days (not necessarily
consecutive). The farmer has only one week (7 days) left to harvest his crop. Given
that the probability of a sunny day is 0.8, what is the probability that the farmer will
be able to get the crop harvested on time?
a. 0.725
b. 0.344
c. 0.176
d. 0.599
*e. 0.275
34. A canoe club sponsor has taken canoeing groups through a particularly rough
section of white water on a mountain river. Past trips and experience of the sponsor
leads her to believe that fifty percent of the canoeists who attempt to paddle their way
through this section will overturn. At the present time, there are five canoes
approaching this treacherous section. Assume that the sponsor’s estimate of the
probability of a canoe overturning in this section of water is accurate. What is the
probability that four of the five canoes will overturn?
a. 0.346
*b. 0.156
c. 0.477
d. 0.985
e. 0.224
35. It is known that three out of every ten financial institutions prefer debt-financing
to equity-financing. A random sample of twenty financial institutions was selected.
What is the probability that exactly 13 of the twenty companies sampled preferred
preferred equity-financing to debt-financing?
a. 0.885
b. 0.995
c. 0.003
*d. 0.164
e. 0.228
36. Cape Town is estimated to have 21% of homes whose owners subscribe to the
satellite television service, DSTV. If a random sample of four homes is taken, what is
the probability that all four homes subscribe to DSTV?
a. 0.2100
b. 0.5000
c. 0.8791
d. 0.0021
*e. 0.0019
37. A canoe club sponsor has taken canoeing groups through a particularly rough
section of white water on a mountain river. Past trips and experience of the sponsor
leads her to believe that fifty percent of the canoeists who attempt to paddle their way
through this section will overturn. At the present time, there are five canoes
approaching this treacherous section. Assume that the sponsor’s estimate of the
probability of a canoe overturning in this section of water is accurate. What is the
probability that less than two of the five canoes will overturn?
*a. 0.187
b. 0.031
c. 0.246
d. 0.317
e. 0.500
38. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that at most 7 of the 10
students got A’s for matric?
*a. 0.617
b. 0.851
c. 0.972
d. 0.474
e. 0.756
39. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that at most 8 of the 10
students got A’s for matric?
a. 0.617
*b. 0.851
c. 0.972
d. 0.474
e. 0.756
40. It is believed that 70% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that at most 9 of the 10
students got A’s for matric?
a. 0.617
b. 0.851
*c. 0.972
d. 0.474
e. 0.756
41. It is believed that 75% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that at most 7 of the 10
students got A’s for matric?
a. 0.617
b. 0.851
c. 0.972
*d. 0.474
e. 0.756
42. It is believed that 75% of STA1000S students got A’s for their final matric exams.
Ten students are randomly chosen. What is the probability that at most 8 of the 10
students got A’s for matric?
a. 0.617
b. 0.851
c. 0.972
d. 0.474
*e. 0.756
43. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that at
most 9 passengers on a full flight check in their luggage?
*a. 0.597
b. 0.966
c. 0.128
d. 0.755
e. 0.278
44. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that at
most 9 passengers on a full flight do not check in their luggage?
a. 0.597
*b. 0.966
c. 0.128
d. 0.755
e. 0.278
45. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 20 passengers. What is the probability that at
most 9 passengers on a full flight check in their luggage?
a. 0.597
b. 0.966
*c. 0.128
d. 0.755
e. 0.278
46. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 20 passengers. What is the probability that at
most 9 passengers on a full flight do not check in their luggage?
a. 0.597
b. 0.966
c. 0.128
*d. 0.755
e. 0.278
47. Thirty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that at
most 9 passengers on a full flight check in their luggage?
a. 0.597
b. 0.966
c. 0.128
d. 0.755
*e. 0.278
48. If X ~ B(6, 0.25), what is P(X < 3)?
*a. 0.831
b. 0.959
c. 0.756
d. 0.577
e. 0.812
49. If X ~ B(6, 0.40), what is P(X < 5)?
a. 0.831
*b. 0.959
c. 0.756
d. 0.577
e. 0.812
50. If X ~ B(7, 0.25), what is P(X < 3)?
a. 0.831
b. 0.959
*c. 0.756
d. 0.577
e. 0.812
51. If X ~ B(7, 0.20), what is P(X < 2)?
a. 0.831
b. 0.959
c. 0.756
*d. 0.577
e. 0.812
52. If X ~ B(5, 0.50), what is P(X < 4)?
a. 0.831
b. 0.959
c. 0.756
d. 0.577
*e. 0.812
53. A study conducted at a certain university shows that 40% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that at least 8 of them will have found a job in their chosen field?
*a. 0.213
b. 0.034
c. 0.390
d. 0.696
e. 0.412
54. A study conducted at a certain university shows that 40% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that at least 10 of them will have found a job in their chosen field?
a. 0.213
*b. 0.034
c. 0.390
d. 0.696
e. 0.412
55. A study conducted at a certain university shows that 40% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that at least 7 of them will have found a job in their chosen field?
a. 0.213
b. 0.034
*c. 0.390
d. 0.696
e. 0.412
56. A study conducted at a certain university shows that 50% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 15
graduates are selected at the university at random one year after graduation. What is
the probability that at least 7 of them will have found a job in their chosen field?
a. 0.213
b. 0.034
c. 0.390
*d. 0.696
e. 0.412
57. A study conducted at a certain university shows that 50% of the university’s
graduates obtain a job in their chosen field within one year after graduation. 20
graduates are selected at the university at random one year after graduation. What is
the probability that at least 11 of them will have found a job in their chosen field?
a. 0.213
b. 0.034
c. 0.390
d. 0.696
*e. 0.412
58. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that 9 or
more passengers on a full flight check in their luggage?
*a. 0.610
b. 0.095
c. 0.944
d. 0.404
e. 0.869
59. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that 9 or
more passengers on a full flight do not check in their luggage?
a. 0.610
*b. 0.095
c. 0.944
d. 0.404
e. 0.869
60. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 20 passengers. What is the probability that 9 or
more passengers on a full flight check in their luggage?
a. 0.610
b. 0.095
*c. 0.944
d. 0.404
e. 0.869
61. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 20 passengers. What is the probability that 9 or
more passengers on a full flight do not check in their luggage?
a. 0.610
b. 0.095
c. 0.944
*d. 0.404
e. 0.869
62. Thirty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. What is the probability that 9 or
more passengers on a full flight check in their luggage?
a. 0.610
b. 0.095
c. 0.944
d. 0.404
*e. 0.869
63. If X ~ B(6, 0.25), what is P(X > 3)?
*a. 0.038
b. 0.004
c. 0.071
d. 0.148
e. 0.031
64. If X ~ B(6, 0.40), what is P(X > 5)?
a. 0.038
*b. 0.004
c. 0.071
d. 0.148
e. 0.031
65. If X ~ B(7, 0.25), what is P(X > 3)?
a. 0.038
b. 0.004
*c. 0.071
d. 0.148
e. 0.031
66. If X ~ B(7, 0.20), what is P(X > 2)?
a. 0.038
b. 0.004
c. 0.071
*d. 0.148
e. 0.031
67. If X ~ B(5, 0.50), what is P(X > 4)?
a. 0.038
b. 0.004
c. 0.071
d. 0.148
*e. 0.031
68. Assume that it is known that 80% of monkeys treated with a specific antibiotic
recover from a particular disease. If 5 monkeys are treated, find the probability that at
least 4 monkeys recover.
a. 0.672
b. 0.328
c. 0.263
*d. 0.737
e. 0.583
69. An important part of the customer service responsibilities of a telephone company
relates to the speed with which problems in residential service can be repaired.
Suppose past data indicate that the probability is 0.5 that problems in residential
service can be repaired on the same day. On a given day 5 problems were reported.
What is the probability that at least three problems will be repaired on the same day?
*a. 0.500
b. 0.031
c. 0.187
d. 0.583
e. 0.261
70. It is known that three out of every ten financial institutions prefer debt-financing
to equity-financing. A random sample of twenty financial institutions was selected.
What is the probability that at least eight financial institutions prefer debt-financing to
equity-financing?
a. 0.7720
b. 0.1130
c. 0.1144
*d. 0.2280
e. 0.8870
71. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the expected number of non-defective CD players out of the sample of 120 CD
players?
a. 6
*b. 114
c. 5
d. 95
e. 120
72. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 120
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 120 CD players selected are defective. What is
the expected number of defective CD players out of the sample of 120 CD players?
*a. 6
b. 114
c. 5
d. 95
e. 120
73. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 100
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 100 CD players selected are defective. What is
the expected number of non-defective CD players out of the sample of 100 CD
players?
a. 6
b. 114
c. 5
*d. 95
e. 120
74. A large manufacturing company that produces CD players believes that 1 out of
every 20 CD players is defective. To ensure quality control, a random sample of 100
CD players were selected and tested. A large quality control investigation would be
launched if more than 10 out of the 100 CD players selected are defective. What is
the expected number of defective CD players out of the sample of 100 CD players?
a. 6
b. 114
*c. 5
d. 95
e. 120
75. At a wholesale protea nursery exactly 100 seeds are planted in each seed-bed, and the probability
that a protea seed will germinate is 0.8. What is the expected number of seeds in the
seed-bed that will germinate?
*a. 80
b. 96
c. 75
d. 160
e. 65
76. At a wholesale protea nursery exactly 120 seeds are planted in each seed-bed, and the probability
that a protea seed will germinate is 0.8. What is the expected number of seeds in the
seed-bed that will germinate?
a. 80
*b. 96
c. 75
d. 160
e. 65
77. At a wholesale protea nursery exactly 100 seeds are planted in each seed-bed, and the probability
that a protea seed will germinate is 0.75. What is the expected number of seeds in the
seed-bed that will germinate?
a. 80
b. 96
*c. 75
d. 160
e. 65
78. At a wholesale protea nursery exactly 200 seeds are planted in each seed-bed, and the probability
that a protea seed will germinate is 0.8. What is the expected number of seeds in the
seed-bed that will germinate?
a. 80
b. 96
c. 75
*d. 160
e. 65
79. At a wholesale protea nursery exactly 100 seeds are planted in each seed-bed, and the probability
that a protea seed will germinate is 0.65. What is the expected number of seeds in the
seed-bed that will germinate?
a. 80
b. 96
c. 75
d. 160
*e. 65
80. What is the expected number of heads in 100 tosses of an unbiased coin?
a. 100
b. 25
*c. 50
d. 75
e. 0
81. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
mean of the number of passengers who do not check in any luggage?
*a. 6.00
b. 6.45
c. 7.20
d. 7.50
e. 4.50
82. 43% percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
mean of the number of passengers who do not check in any luggage?
a. 6.00
*b. 6.45
c. 7.20
d. 7.50
e. 4.50
83. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 18 passengers. For a full flight, what is the
mean of the number of passengers who do not check in any luggage?
a. 6.00
b. 6.45
*c. 7.20
d. 7.50
e. 4.50
84. Fifty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
mean of the number of passengers who do not check in any luggage?
a. 6.00
b. 6.45
c. 7.20
*d. 7.50
e. 4.50
85. 25% percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 18 passengers. For a full flight, what is the
mean of the number of passengers who do not check in any luggage?
a. 6.00
b. 6.45
c. 7.20
d. 7.50
*e. 4.50
86. A recent survey in Cape Town revealed that 60% of the vehicles traveling on
highways, where speed limits are posted at 80 km per hour, were exceeding the limit.
Suppose you randomly record the speeds of 10 vehicles traveling on the N1 where the
speed limit is 80 km per hour. What is the mean or expected number of vehicles who
will exceed the speed limit in this sample?
a. 10
b. 4
*c. 6
d. 1
e. 8
87. Cape Town is estimated to have 21% of homes whose owners subscribe to the
satellite television service, DSTV. If a random sample of four homes is taken, what is
the mean number of homes in this sample that subscribe to DSTV?
*a. 0.84
b. 1.00
c. 2.00
d. 0.21
e. 1.68
88. An important part of the customer service responsibilities of a telephone company
relates to the speed with which problems in residential service can be repaired.
Suppose past data indicate that the probability is 0.5 that problems in residential
service can be repaired on the same day. On a given day 5 problems were reported.
What is the standard deviation of the random variable describing the number of same
day repairs in this sample?
a. -0.500
b. 0.500
c. 1.500
*d. 1.118
e. 1.250
89. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
variance of the number of passengers who do not check in any luggage?
*a. 3.60
b. 3.68
c. 4.32
d. 3.75
e. 3.38
90. 43% percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
variance of the number of passengers who do not check in any luggage?
a. 3.60
*b. 3.68
c. 4.32
d. 3.75
e. 3.38
91. Forty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 18 passengers. For a full flight, what is the
variance of the number of passengers who do not check in any luggage?
a. 3.60
b. 3.68
*c. 4.32
d. 3.75
e. 3.38
92. Fifty percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 15 passengers. For a full flight, what is the
variance of the number of passengers who do not check in any luggage?
a. 3.60
b. 3.68
c. 4.32
*d. 3.75
e. 3.38
93. 25% percent of the passengers who fly on a certain route do not check in any
luggage. The planes on this route seat 18 passengers. For a full flight, what is the
variance of the number of passengers who do not check in any luggage?
a. 3.60
b. 3.68
c. 4.32
d. 3.75
*e. 3.38
94. It is believed that 70% of STA1000S students got A’s for their final matric exams.
What is the standard deviation of the number of students who got A’s for matric, in
samples of size 10?
*a. 1.45
b. 2.10
c. 1.37
d. 1.88
e. 3.85
95. It is believed that 70% of STA1000S students got A’s for their final matric exams.
What is the variance of the number of students who got A’s for matric, in samples of
size 10?
a. 1.45
*b. 2.10
c. 1.37
d. 1.88
e. 3.85
96. It is believed that 75% of STA1000S students got A’s for their final matric exams.
What is the standard deviation of the number of students who got A’s for matric, in
samples of size 10?
a. 1.45
b. 2.10
*c. 1.37
d. 1.88
e. 3.85
97. It is believed that 75% of STA1000S students got A’s for their final matric exams.
What is the variance of the number of students who got A’s for matric, in samples of
size 10?
a. 1.45
b. 2.10
c. 1.37
*d. 1.88
e. 3.85
98. It is believed that 70% of STA1000S students got A’s for their final matric exams.
What is the standard deviation of the number of students who got A’s for matric, in
samples of size 20?
*a. 2.05
b. 4.20
c. 1.26
d. 1.60
e. 3.85
99. It is believed that 70% of STA1000S students got A’s for their final matric exams.
What is the variance of the number of students who got A’s for matric, in samples of
size 20?
a. 2.05
*b. 4.20
c. 1.26
d. 1.60
e. 3.85
100. It is believed that 80% of STA1000S students got A’s for their final matric
exams. What is the standard deviation of the number of students who got A’s for
matric, in samples of size 10?
a. 2.05
b. 4.20
*c. 1.26
d. 1.60
e. 3.85
101. It is believed that 80% of STA1000S students got A’s for their final matric
exams. What is the variance of the number of students who got A’s for matric, in
samples of size 10?
a. 2.05
b. 4.20
c. 1.26
*d. 1.60
e. 3.85
102. It is believed that 70% of STA1000S students got A’s for their final matric
exams. What is the standard deviation of the number of students who got A’s for
matric, in samples of size 15?
*a. 1.77
b. 4.20
c. 1.26
d. 1.60
e. 3.15
103. It is believed that 70% of STA1000S students got A’s for their final matric
exams. What is the variance of the number of students who got A’s for matric, in
samples of size 15?
a. 1.77
b. 4.20
c. 1.26
d. 1.60
*e. 3.15
104. Which of the following is not a characteristic of a Binomial distribution?
a. There is a sequence of identical trials
b. The trials are independent of one another
*c. Each trial results in two or more outcomes
d. The probability of success (p) is the same for all trials
e. There are a finite number of trials
105. A computer that operates continuously breaks down randomly on average 6
times per month (ie: 4 weeks). What is the probability of exactly 4 breakdowns in the
first two weeks?
*a. 0.168
b. 0.134
c. 0.815
d. 0.285
e.0.547
106. A computer that operates continuously breaks down randomly on average 6
times per month (ie: 4 weeks). What is the probability of exactly 4 breakdowns in the
first month?
a. 0.168
*b. 0.134
c. 0.815
d. 0.285
e. 0.547
107. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that exactly ten tourists arrive within the first hour?
*a. 0.105
b. 0.114
c. 0.066
d. 0.041
e. 0.161
108. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that exactly eleven tourists arrive within the first
hour?
a. 0.105
*b. 0.114
c. 0.066
d. 0.041
e. 0.161
109. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that exactly eight tourists arrive within the first
hour?
a. 0.105
b. 0.114
*c. 0.066
d. 0.041
e. 0.161
110. Tourists enter a popular game reserve at an average rate of one every ten
minutes. What is the probability that exactly ten tourists arrive within the first hour?
a. 0.105
b. 0.114
c. 0.066
*d. 0.041
e. 0.161
111. Tourists enter a popular game reserve at an average rate of one every ten
minutes. What is the probability that exactly five tourists arrive within the first hour?
a. 0.105
b. 0.114
c. 0.066
d. 0.041
*e. 0.161
112. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that it takes more than ten minutes until the first
tourist arrives?
*a. 0.135
b. 0.050
c. 0.368
d. 0.018
e. 0.002
113. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that it takes more than fifteen minutes until the first
tourist arrives?
a. 0.135
*b. 0.050
c. 0.368
d. 0.018
e. 0.002
114. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that it takes more than five minutes until the first
tourist arrives?
a. 0.135
b. 0.050
*c. 0.368
d. 0.018
e. 0.002
115. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that it takes more than twenty minutes until the first
tourist arrives?
a. 0.135
b. 0.050
c. 0.368
*d. 0.018
e. 0.002
116. Tourists enter a popular game reserve at an average rate of one every five
minutes. What is the probability that it takes more than half an hour until the first
tourist arrives?
a. 0.135
b. 0.050
c. 0.368
d. 0.018
*e. 0.002
117. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that exactly 5 tickets are written on a randomly selected day?
*a. 0.109
b. 0.146
c. 0.137
d. 0.149
e. 0.128
118. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that exactly 7 tickets are written on a randomly selected day?
a. 0.109
*b. 0.146
c. 0.137
d. 0.149
e. 0.128
119. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that exactly 8 tickets are written on a randomly selected day?
a. 0.109
b. 0.146
*c. 0.137
d. 0.149
e. 0.128
120. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7 tickets per day. What is the
probability that exactly 6 tickets are written on a randomly selected day?
a. 0.109
b. 0.146
c. 0.137
*d. 0.149
e. 0.128
121. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7 tickets per day. What is the
probability that exactly 5 tickets are written on a randomly selected day?
a. 0.109
b. 0.146
c. 0.137
d. 0.149
*e. 0.128
122. Seventy (70) accidents are reported on a particular stretch of highway over a 90day period. Assume that this trend continues and that the accidents occur at random
with an average rate of 70 accidents per 90 days. What is the probability that there
will be no accidents reported for a whole week (assume a seven-day week)?
*a. 0.0043
b. 0.0020
c. 0.0074
d. 0.0037
e. 0.0022
123. Eighty (80) accidents are reported on a particular stretch of highway over a 90day period. Assume that this trend continues and that the accidents occur at random
with an average rate of 80 accidents per 90 days. What is the probability that there
will be no accidents reported for a whole week (assume a seven-day week)?
a. 0.0043
*b. 0.0020
c. 0.0074
d. 0.0037
e. 0.0022
124. Seventy (70) accidents are reported on a particular stretch of highway over a
100-day period. Assume that this trend continues and that the accidents occur at
random with an average rate of 70 accidents per 100 days. What is the probability that
there will be no accidents reported for a whole week (assume a seven-day week)?
a. 0.0043
b. 0.0020
*c. 0.0074
d. 0.0037
e. 0.0022
125. Eighty (80) accidents are reported on a particular stretch of highway over a 100day period. Assume that this trend continues and that the accidents occur at random
with an average rate of 80 accidents per 100 days. What is the probability that there
will be no accidents reported for a whole week (assume a seven-day week)?
a. 0.0043
b. 0.0020
c. 0.0074
*d. 0.0037
e. 0.0022
126. Seventy (70) accidents are reported on a particular stretch of highway over a 80day period. Assume that this trend continues and that the accidents occur at random
with an average rate of 70 accidents per 80 days. What is the probability that there
will be no accidents reported for a whole week (assume a seven-day week)?
a. 0.0043
b. 0.0020
c. 0.0074
d. 0.0037
*e. 0.0022
127. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain exactly four colonies?
*a. 0.195
b. 0.156
c. 0.175
d. 0.146
e. 0.161
128. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain exactly five colonies?
a. 0.195
*b. 0.156
c. 0.175
d. 0.146
e. 0.161
129. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish.
What is the probability that the next dish studied will contain exactly five colonies?
a. 0.195
b. 0.156
*c. 0.175
d. 0.146
e. 0.161
130. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish.
What is the probability that the next dish studied will contain exactly six colonies?
a. 0.195
b. 0.156
c. 0.175
*d. 0.146
e. 0.161
131. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are six colonies per dish.
What is the probability that the next dish studied will contain exactly six colonies?
a. 0.195
b. 0.156
c. 0.175
d. 0.146
*e. 0.161
132. If X is a random variable such that X ~ P(3.5), what is P(X = 5)?
*a. 0.133
b. 0.185
c. 0.161
d. 0.045
e. 0.171
133. If X is a random variable such that X ~ P(3.5), what is P(X = 2)?
a. 0.133
*b. 0.185
c. 0.161
d. 0.045
e. 0.171
134. If X is a random variable such that X ~ P(6), what is P(X = 5)?
a. 0.133
b. 0.185
*c. 0.161
d. 0.045
e. 0.171
135. If X is a random variable such that X ~ P(6), what is P(X = 2)?
a. 0.133
b. 0.185
c. 0.161
*d. 0.045
e. 0.171
136. If X is a random variable such that X ~ P(5.5), what is P(X = 5)?
a. 0.133
b. 0.185
c. 0.161
d. 0.045
*e. 0.171
137. Meticulous record keeping over a long period of time shows that doctors in a
busy community medical practice encounter a patient infected with Ebola virus once
every year on average. This practice is suddenly confronted with three patients
infected with Ebola virus over a period of six months. What is the probability of this
happening if there has been no change in the incidence of Ebola virus in the
community?
*a. 0.012
b. 0.061
c. 0.076
d. 0.184
e. 0.016
138. Meticulous record keeping over a long period of time shows that doctors in a
busy community medical practice encounter a patient infected with Ebola virus twice
every year on average. This practice is suddenly confronted with three patients
infected with Ebola virus over a period of six months. What is the probability of this
happening if there has been no change in the incidence of Ebola virus in the
community?
a. 0.012
*b. 0.061
c. 0.076
d. 0.184
e. 0.016
139. Meticulous record keeping over a long period of time shows that doctors in a
busy community medical practice encounter a patient infected with Ebola virus once
every year on average. This practice is suddenly confronted with two patients infected
with Ebola virus over a period of six months. What is the probability of this
happening if there has been no change in the incidence of Ebola virus in the
community?
a. 0.012
b. 0.061
*c. 0.076
d. 0.184
e. 0.016
140. Meticulous record keeping over a long period of time shows that doctors in a
busy community medical practice encounter a patient infected with Ebola virus twice
every year on average. This practice is suddenly confronted with two patients infected
with Ebola virus over a period of six months. What is the probability of this
happening if there has been no change in the incidence of Ebola virus in the
community?
a. 0.012
b. 0.061
c. 0.076
*d. 0.184
e. 0.016
141. Assume that during the Cape Town Argus Pick ‘n Pay cycle tour accidents occur
on average 3 times per 10 km stretch. What is the probability that it is more than 5 km
before the next accident?
a. 0.777
*b. 0.223
c. 0.741
d. 0.259
e. 0.521
142. Car accidents occur in South Africa at an average rate of 72 accidents per hour.
What is the probability that it will be more than 3 minutes before the next accident
occurs?
a. 0.877
b. 0.651
c. 0.131
*d. 0.027
e. 0.584
143. A dispatcher for an airport shuttle will send a van to the airport on average twice
per hour during the Soccer World Cup in 2010. The distribution is expected to be
Poisson, and the driver must take a 15- minute lunch break. The probability that he
can complete his lunch break before receiving a call is:
a. 0.135
*b. 0.607
c. 0.394
d. 1.649
e. 0.865
144. A dispatcher for an airport shuttle will send a van to the airport on average twice
per hour during the Soccer World Cup in 2010. The distribution is expected to be
Poisson, and the driver must take a 15- minute lunch break. The probability that he
gets 2 calls (dispatches) in 30 minutes is:
*a. 0.184
b. 0.465
c. 0.234
d. 0.314
e. 0.000
145. In a public library, books are lost and have to be replaced at an average rate of
2.75 books per week. What is the probability that in a given month (4 weeks) 10
books are lost?
a. 0.460
*b. 0.119
c. 0.275
d. 0.435
e. 0.357
146. In a public library, books are lost and have to be replaced at an average rate of
2.75 books per week. What is the probability that it will be more than one week
before the next book is lost?
a. 0.690
b. 0.340
*c. 0.064
d. 0.284
e. 0.170
147. A drop of water from a lake contains on average 0.5 bacteria per drop. A small
dish containing 4 drops of water from this lake is placed under the microscope. What
is the probability of observing at most 1 bacterium in this dish?
*a. 0.406
b. 0.594
c. 0.092
d. 0.938
e. 0.910
148. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that less than 6 tickets are written on a randomly selected day?
*a. 0.241
b. 0.301
c. 0.378
d. 0.132
e. 0.450
149. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7 tickets per day. What is the
probability that less than 6 tickets are written on a randomly selected day?
a. 0.241
*b. 0.301
c. 0.378
d. 0.132
e. 0.450
150. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that less than 7 tickets are written on a randomly selected day?
a. 0.241
b. 0.301
*c. 0.378
d. 0.132
e. 0.450
151. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7.5 tickets per day. What is the
probability that less than 5 tickets are written on a randomly selected day?
a. 0.241
b. 0.301
c. 0.378
*d. 0.132
e. 0.450
152. The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted level. Suppose the number of tickets written per day
follows a Poisson distribution with a mean of 7 tickets per day. What is the
probability that less than 7 tickets are written on a randomly selected day?
a. 0.241
b. 0.301
c. 0.378
d. 0.132
*e. 0.450
153. A local motor vehicle break-down service must respond to, on average, 10 calls
per day in order to keep revenues at the budgeted level. Suppose the number of calls
received from customers per day follows a Poisson distribution with a mean of 11
calls per day. What is the probability that at most 10 calls will be received on a
randomly selected day?
*a. 0.460
b. 0.232
c. 0.347
d. 0.576
e. 0.689
154. A local motor vehicle break-down service must respond to, on average, 10 calls
per day in order to keep revenues at the budgeted level. Suppose the number of calls
received from customers per day follows a Poisson distribution with a mean of 11
calls per day. What is the probability that at most 8 calls will be received on a
randomly selected day?
a. 0.460
*b. 0.232
c. 0.347
d. 0.576
e. 0.689
155. A local motor vehicle break-down service must respond to, on average, 10 calls
per day in order to keep revenues at the budgeted level. Suppose the number of calls
received from customers per day follows a Poisson distribution with a mean of 12
calls per day. What is the probability that at most 10 calls will be received on a
randomly selected day?
a. 0.460
b. 0.232
*c. 0.347
d. 0.576
e. 0.689
156. A local motor vehicle break-down service must respond to, on average, 10 calls
per day in order to keep revenues at the budgeted level. Suppose the number of calls
received from customers per day follows a Poisson distribution with a mean of 12
calls per day. What is the probability that at most 12 calls will be received on a
randomly selected day?
a. 0.460
b. 0.232
c. 0.347
*d. 0.576
e. 0.689
157. A local motor vehicle break-down service must respond to, on average, 10 calls
per day in order to keep revenues at the budgeted level. Suppose the number of calls
received from customers per day follows a Poisson distribution with a mean of 11
calls per day. What is the probability that at most 12 calls will be received on a
randomly selected day?
a. 0.460
b. 0.232
c. 0.347
d. 0.576
*e. 0.689
158. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain two or fewer colonies?
*a. 0.238
b. 0.433
c. 0.125
d. 0.265
e. 0.285
159. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain three or fewer colonies?
a. 0.238
*b. 0.433
c. 0.125
d. 0.265
e. 0.285
160. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish.
What is the probability that the next dish studied will contain two or fewer colonies?
a. 0.238
b. 0.433
*c. 0.125
d. 0.265
e. 0.285
161. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish
What is the probability that the next dish studied will contain three or fewer colonies?
a. 0.238
b. 0.433
c. 0.125
*d. 0.265
e. 0.285
162. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are six colonies per dish.
What is the probability that the next dish studied will contain four or fewer colonies?
a. 0.238
b. 0.433
c. 0.125
d. 0.265
*e. 0.285
163. A random variable, X, follows a Poisson distribution with a standard deviation of
3. What is P(X < 5)?
*a. 0.055
b. 0.815
c. 0.238
d. 0.440
e. 0.151
164. A random variable, X, follows a Poisson distribution with a variance of 3. What
is P(X < 5)?
a. 0.055
*b. 0.815
c. 0.238
d. 0.440
e. 0.151
165. A random variable, X, follows a Poisson distribution with a standard deviation of
2. What is P(X < 3)?
a. 0.055
b. 0.815
*c. 0.238
d. 0.440
e. 0.151
166. A random variable, X, follows a Poisson distribution with a variance of 5. What
is P(X < 5)?
a. 0.055
b. 0.815
c. 0.238
*d. 0.440
e. 0.151
167. A random variable, X, follows a Poisson distribution with a variance of 6. What
is P(X < 4)?
a. 0.055
b. 0.815
c. 0.238
d. 0.440
*e. 0.151
168. If X is a random variable such that X ~ P(3.5), what is P(X ≤ 5)?
*a. 0.858
b. 0.321
c. 0.446
d. 0.062
e. 0.529
169. If X is a random variable such that X ~ P(3.5), what is P(X ≤ 2)?
a. 0.858
*b. 0.321
c. 0.446
d. 0.062
e. 0.529
170. If X is a random variable such that X ~ P(6), what is P(X ≤ 5)?
a. 0.858
b. 0.321
*c. 0.446
d. 0.062
e. 0.529
171. If X is a random variable such that X ~ P(6), what is P(X ≤ 2)?
a. 0.858
b. 0.321
c. 0.446
*d. 0.062
e. 0.529
172. If X is a random variable such that X ~ P(5.5), what is P(X ≤ 5)?
a. 0.858
b. 0.321
c. 0.446
d. 0.062
*e. 0.529
173. Cars arrive at an Engen petrol station at an average rate of 10 cars per hour.
What is the probability that less than 4 cars arrive in 30 minutes?
*a. 0.265
b. 0.433
c. 0.857
d. 0.532
e. 0.406
174. Cars arrive at an Engen petrol station at an average rate of 8 cars per hour. What
is the probability that less than 4 cars arrive in 30 minutes?
a. 0.265
*b. 0.433
c. 0.857
d. 0.532
e. 0.406
175. Cars arrive at an Engen petrol station at an average rate of 6 cars per hour. What
is the probability that less than 4 cars arrive in 20 minutes?
a. 0.265
b. 0.433
*c. 0.857
d. 0.532
e. 0.406
176. Cars arrive at an Engen petrol station at an average rate of 9 cars per hour. What
is the probability that less than 5 cars arrive in 30 minutes?
a. 0.265
b. 0.433
c. 0.857
*d. 0.532
e. 0.406
177. Cars arrive at an Engen petrol station at an average rate of 12 cars per hour.
What is the probability that less than 2 cars arrive in 10 minutes?
a. 0.265
b. 0.433
c. 0.857
d. 0.532
*e. 0.406
178. A local police station receives on average 8 emergency telephone calls per hour.
What is the probability that the station will get at least 4 calls per hour?
a. 0.039
b. 0.094
c. 0.905
*d. 0.958
e. 0.963
179. Seventy (70) accidents are reported on a particular stretch of highway over a 90day period. What is the probability that there will be more than one accident during a
week (assume a seven-day week)?
*a. 0.9722
b. 0.9857
c. 0.9561
d. 0.9756
e. 0.9844
180. Eighty (80) accidents are reported on a particular stretch of highway over a 90day period. What is the probability that there will be more than one accident during a
week (assume a seven-day week)?
a. 0.9722
*b. 0.9857
c. 0.9561
d. 0.9756
e. 0.9844
181. Seventy (70) accidents are reported on a particular stretch of highway over a
100-day period. What is the probability that there will be more than one accident
during a week (assume a seven-day week)?
a. 0.9722
b. 0.9857
*c. 0.9561
d. 0.9756
e. 0.9844
182. Eighty (80) accidents are reported on a particular stretch of highway over a 100day period. What is the probability that there will be more than one accident during a
week (assume a seven-day week)?
a. 0.9722
b. 0.9857
c. 0.9561
*d. 0.9756
e. 0.9844
183. Seventy (70) accidents are reported on a particular stretch of highway over a 80day period. What is the probability that there will be more than one accident during a
week (assume a seven-day week)?
a. 0.9722
b. 0.9857
c. 0.9561
d. 0.9756
*e. 0.9844
184. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain at least two colonies?
*a. 0.908
b. 0.762
c. 0.960
d. 0.875
e. 0.849
185. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are four colonies per dish.
What is the probability that the next dish studied will contain at least three colonies?
a. 0.908
*b. 0.762
c. 0.960
d. 0.875
e. 0.849
186. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish.
What is the probability that the next dish studied will contain at least two colonies?
a. 0.908
b. 0.762
*c. 0.960
d. 0.875
e. 0.849
187. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are five colonies per dish
What is the probability that the next dish studied will contain at least three colonies?
a. 0.908
b. 0.762
c. 0.960
*d. 0.875
e. 0.849
188. In checking river water samples for bacteria, water is placed in a culture medium
in order to grow colonies of bacteria. The number of colonies seen in a dish is a
random variable, X. Scientists know that on average there are six colonies per dish.
What is the probability that the next dish studied will contain at least four colonies?
a. 0.908
b. 0.762
c. 0.960
d. 0.875
*e. 0.849
189. A random variable, X, follows a Poisson distribution with a standard deviation of
3. What is P(X > 5)?
*a. 0.884
b. 0.084
c. 0.567
d. 0.384
e. 0.715
190. A random variable, X, follows a Poisson distribution with a variance of 3. What
is P(X > 5)?
a. 0.884
*b. 0.084
c. 0.567
d. 0.384
e. 0.715
191. A random variable, X, follows a Poisson distribution with a standard deviation of
2. What is P(X > 3)?
a. 0.884
b. 0.084
*c. 0.567
d. 0.384
e. 0.715
192. A random variable, X, follows a Poisson distribution with a variance of 5. What
is P(X > 5)?
a. 0.884
b. 0.084
c. 0.567
*d. 0.384
e. 0.715
193. A random variable, X, follows a Poisson distribution with a variance of 6. What
is P(X > 4)?
a. 0.884
b. 0.084
c. 0.567
d. 0.384
*e. 0.715
194. If X is a random variable such that X ~ P(3.5), what is P(X ≥ 5)?
*a. 0.275
b. 0.864
c. 0.715
d. 0.983
e. 0.642
195. If X is a random variable such that X ~ P(3.5), what is P(X ≥ 2)?
a. 0.275
*b. 0.864
c. 0.715
d. 0.983
e. 0.642
196. If X is a random variable such that X ~ P(6), what is P(X ≥ 5)?
a. 0.275
b. 0.864
*c. 0.715
d. 0.983
e. 0.642
197. If X is a random variable such that X ~ P(6), what is P(X ≥ 2)?
a. 0.275
b. 0.864
c. 0.715
*d. 0.983
e. 0.642
198. If X is a random variable such that X ~ P(5.5), what is P(X ≥ 5)?
a. 0.275
b. 0.864
c. 0.715
d. 0.983
*e. 0.642
199. Cars arrive at an Engen petrol station at an average rate of 10 cars per hour.
What is the probability that more than 4 cars arrive in 30 minutes?
*a. 0.560
b. 0.371
c. 0.053
d. 0.297
e. 0.323
200. Cars arrive at an Engen petrol station at an average rate of 8 cars per hour. What
is the probability that more than 4 cars arrive in 30 minutes?
a. 0.560
*b. 0.371
c. 0.053
d. 0.297
e. 0.323
201. Cars arrive at an Engen petrol station at an average rate of 6 cars per hour. What
is the probability that more than 4 cars arrive in 20 minutes?
a. 0.560
b. 0.371
*c. 0.053
d. 0.297
e. 0.323
202. Cars arrive at an Engen petrol station at an average rate of 9 cars per hour. What
is the probability that more than 5 cars arrive in 30 minutes?
a. 0.560
b. 0.371
c. 0.053
*d. 0.297
e. 0.323
203. Cars arrive at an Engen petrol station at an average rate of 12 cars per hour.
What is the probability that more than 2 cars arrive in 10 minutes?
a. 0.560
b. 0.371
c. 0.053
d. 0.297
*e. 0.323
204. A computer that operates continuously breaks down randomly on average 6
times per month (4 weeks). What is the expected number of breakdowns in 3 weeks?
*a. 4.5
b. 6.0
c. 3.0
d. 12.0
e. 9.0
205. A computer that operates continuously breaks down randomly on average 6
times per month (4 weeks). What is the expected number of breakdowns in one
month?
a. 4.5
*b. 6.0
c. 3.0
d. 12.0
e. 9.0
206. A computer that operates continuously breaks down randomly on average 6
times per month (4 weeks). What is the expected number of breakdowns in 2 weeks?
a. 4.5
b. 6.0
*c. 3.0
d. 12.0
e. 9.0
207. A computer that operates continuously breaks down randomly on average 6
times per month (4 weeks). What is the expected number of breakdowns in 8 weeks?
a. 4.5
b. 6.0
c. 3.0
*d. 12.0
e. 9.0
208. A computer that operates continuously breaks down randomly on average 6
times per month (4 weeks). What is the expected number of breakdowns in 6 weeks?
a. 4.5
b. 6.0
c. 3.0
d. 12.0
*e. 9.0
209. Tourists enter a popular game reserve at an average rate of one every five
minutes. Each tourist is required to pay a cover charge of R10 per head. The cover
charge is the only source of income for the game reserve. What is the expected
income for the game reserve in an 8-hour day?
*a. R960
b. R1920
c. R6720
d. R13440
e. R2880
210. Tourists enter a popular game reserve at an average rate of one every five
minutes. Each tourist is required to pay a cover charge of R20 per head. The cover
charge is the only source of income for the game reserve. What is the expected
income for the game reserve in an 8-hour day?
a. R960
*b. R1920
c. R6720
d. R13440
e. R2880
211. Tourists enter a popular game reserve at an average rate of one every five
minutes. Each tourist is required to pay a cover charge of R10 per head. The cover
charge is the only source of income for the game reserve. What is the expected
income for the game reserve in a week (consisting of 7 days for which the reserve is
open 8 hours per day)?
a. R960
b. R1920
*c. R6720
d. R13440
e. R2880
212. Tourists enter a popular game reserve at an average rate of one every five
minutes. Each tourist is required to pay a cover charge of R20 per head. The cover
charge is the only source of income for the game reserve. What is the expected
income for the game reserve in a week (consisting of 7 days for which the reserve is
open 8 hours per day)?
a. R960
b. R1920
c. R6720
*d. R13440
e. R2880
213. Tourists enter a popular game reserve at an average rate of one every five
minutes. Each tourist is required to pay a cover charge of R10 per head. The cover
charge is the only source of income for the game reserve. What is the expected
income for the game reserve over three 8-hour days?
a. R960
b. R1920
c. R6720
d. R13440
*e. R2880
214. A random variable, X, follows a Poisson distribution with a standard deviation of
3. What is the expected value of X?
*a. 9
b. 3
c. 16
d. 5
e. 4
215. A random variable, X, follows a Poisson distribution with a variance of 3. What
is the expected value of X?
a. 9
*b. 3
c. 16
d. 5
e. 4
216. A random variable, X, follows a Poisson distribution with a standard deviation of
4. What is the expected value of X?
a. 9
b. 3
*c. 16
d. 5
e. 4
217. A random variable, X, follows a Poisson distribution with a variance of 5. What
is the expected value of X?
a. 9
b. 3
c. 16
*d. 5
e. 4
218. A random variable, X, follows a Poisson distribution with a standard deviation of
2. What is the expected value of X?
a. 9
b. 3
c. 16
d. 5
*e. 4
219. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R5.50
is required per car to be allowed to pass through the tollgate, what are the expected
earnings of the tollgate in a 12-hour period?
*a. R792
b. R936
c. R528
d. R660
e. R1584
220. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R6.50
is required per car to be allowed to pass through the tollgate, what are the expected
earnings of the tollgate in a 12-hour period?
a. R792
*b. R936
c. R528
d. R660
e. R1584
221. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R5.50
is required per car to be allowed to pass through the tollgate, what are the expected
earnings of the tollgate in a 8-hour period?
a. R792
b. R936
*c. R528
d. R660
e. R1584
222. Cars arrive at a tollgate at an average rate of 10 cars per hour. If a fee of R5.50
is required per car to be allowed to pass through the tollgate, what are the expected
earnings of the tollgate in a 12-hour period?
a. R792
b. R936
c. R528
*d. R660
e. R1584
223. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R5.50
is required per car to be allowed to pass through the tollgate, what are the expected
earnings of the tollgate in a 24-hour period?
a. R792
b. R936
c. R528
d. R660
*e. R1584
224. X is a random variable such that X ~ P(4). What is the standard deviation of X?
*a. 2
b. 4
c. 3
d. 5
e. 10
225. X is a random variable such that X ~ P(16). What is the standard deviation of X?
a. 2
*b. 4
c. 3
d. 5
e. 10
226. X is a random variable such that X ~ P(9). What is the standard deviation of X?
a. 2
b. 4
*c. 3
d. 5
e. 10
227. X is a random variable such that X ~ P(25). What is the standard deviation of X?
a. 2
b. 4
c. 3
*d. 5
e. 10
228. X is a random variable such that X ~ P(100). What is the standard deviation of
X?
a. 2
b. 4
c. 3
d. 5
*e. 10
229. Cars arrive at a BP petrol station at an average rate of 32 cars per hour. What is
the standard deviation of the number of cars that arrive within half an hour?
*a. 4
b. 16
c. 2
d. 5
e. 25
230. Cars arrive at a BP petrol station at an average rate of 32 cars per hour. What is
the variance of the number of cars that arrive within half an hour?
a. 4
*b. 16
c. 2
d. 5
e. 25
231. Cars arrive at a BP petrol station at an average rate of 16 cars per hour. What is
the standard deviation of the number of cars that arrive within quarter of an hour?
a. 4
b. 16
*c. 2
d. 5
e. 25
232. Cars arrive at a BP petrol station at an average rate of 50 cars per hour. What is
the standard deviation of the number of cars that arrive within half an hour?
a. 4
b. 16
c. 2
*d. 5
e. 25
233. Cars arrive at a BP petrol station at an average rate of 50 cars per hour. What is
the variance of the number of cars that arrive within half an hour?
a. 4
b. 16
c. 2
d. 5
*e. 25
234. A local police station receives on average 8 emergency telephone calls per hour.
What is the standard deviation of the number of calls received in half an hour?
a. 4.00
b. 16.0
c. 8.00
d. 2.83
*e. 2.00
235. In a public library, books are lost and have to be replaced at an average rate of
2.75 books per week. What is the variance of the number of books lost in a two-week
period?
a. 2.75
b. 11.00
*c. 5.50
d. 8.25
e. none of the above
236. Which of the following cannot be modelled by a Poisson distribution?
*a. The number of children watching a movie at a given point in time
b. The number of telephone calls received by a switchboard in an hour
c. The number of customers arriving at a petrol station on Christmas day
d. The number of bacteria found per square metre of soil
e. The number of patients arriving at a hospital in a week