STATISTICS ─CHAPTER 5 TEST
Name
1. A discrete random variable is a random variable that:
a. is derived from a random population
c. can assume any value in one or more intervals
b. is determined by random probability
d. consists of countable values
2. Which of the following is true for the probability of a discrete random variable x?
a. P(x) < 0
b. P(x) > 1
c. P(x) = 2
d. 0 ≤ P(x) ≤ 1
3. Which of the following is true for the probability distribution of a discrete random variable x?
a. Σ P(x) < 0
b. Σ P(x) = 1
c. ΣP(x) = 2
d. ΣP(x) > I
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The following table lists the probability distribution of a discrete random variable x.
x
P(x)
0
.04
1
.11
2
.18
3
.24
4
.14
5
.17
6
.09
Use the above information to answer questions 4, 5, 6, and 7.
4. The probability that x is less than 5 is:
a. .71
b. .88
c. .14
d. .17
5. The probability that x is greater than 3 is:
a. .67
b. .24
c. .57
d. .43
6. The probability that x assumes a value from 2 to 5 is:
a. .17
b. .73
c. .38
d. .12
7. The standard deviation of the random variable x is approximately:
a. 2.97
b. 14.19
c. 6.91
d. 1.72
7
.03
8. The following table lists the probability distribution of a discrete random variable x.
x
P(x)
2
.15
3
.32
4
.24
5
.13
6
.08
7
.06
b. 3.93 c. 4.20
8
.02
The mean of the random variable x is:
a. 2.71
d. 1.96
9. In general, “n factorial” represents:
a. the product of any n numbers
b. the sum of all integers from n to1
c. the product of all integers from n to 1
d. n – 1
10. The factorial of 8 is:
a. 36
b. 40,320
c. 5040
d. 35
11. The factorial of (13 – 7) is:
a. 720
b. 21
c. 120
d. 20
12. The number of combinations for selecting 7 elements from 10 distinct elements is:
a. 70
b. 120
c. 3
d. 100
13. A jury of five persons will be randomly selected from a group of 15 persons. The total number
of combinations are:
a. 3,628,800
b. 5005
c. 3003
d. 120
14. Which of the following is not a condition of the binomial experiment?
a. There are only two trials
b. Each trial has two and only two outcomes
c. p is the probability of success, q is the probability of failure, and p + q = 1
d. The trials are independent
15. The binomial probability distribution is symmetric if:
a. p is equal to .25
b. p is equal to .50
c. p is less than .50
d. p is greater than .50
16. The binomial probability distribution is skewed to the right if:
a. p is .25 or smaller
b. p is .50
c. p is less than .50
d. p is greater than .50
17. Which of the following is an example of a binomial experiment?
a. Rolling a die 10 times and observing for a number
b. Selecting 5 persons and observing whether they are in favor of an issue, against it, or have no
opinion
c. Tossing a coin 20 times and observing for a head or a tail
d. Drawing three marbles from a box that contains red, blue, and yellow marbles
18. Eight percent of all college graduates hired by companies stay with the same company for
more than five years. The probability that in a random sample of 12 such college graduates
hired recently by companies, exactly two will stay with the same company for more than five
years is:
a. .1294
b. .2301
c. .1835
d. .3305
19. Thirty two percent of adults did not visit their physicians’ offices last year. Let x be the
number of adults in a random sample of 15 adults who did not visit their physicians’ offices
last year. The mean of the probability distribution of x is:
a. 32.0
b. 6.2
c. 4.8
d. 3.2
20. Thirty two percent of adults did not visit their physicians, offices last year. Let x be the
number of adults in a random sample of 15 adults who did not visit their physicians’ offices
last year. The standard deviation of the probability distribution of x is approximately:
a. 3.26
b. 4.80
c. 3.20
d. 1.81
21. Which of the following is not a condition to apply the hypergeometric probability
distribution?
a. x is a discrete random variable
c. There are r identical occurrences in the
population
b. The occurrences are random
d. The occurrences are independent
22. For N = 7, r = 3, and n = 5, the probability of x = 0 is:
a. .1905
b. .0288
c. .5714
d. .3334
23. For N = 7, r = 3, and n = 5, the probability P(x < 2) is:
a. .1905
b. .1429
c. .0780
d. .3334
24. For N = 9, r = 4, and n = 6, the probability P(x > 3) is:
a. .9206
b. .0794
c. .0397
d. .9603
25. Let x denote the number of corporations in a random sample of 4 that provide retirement
benefits. Then x is a hypergeometric random variable with N = 16, r = 3, and n = 4. The
probability that at most one of the selected firms offers retirement benfits is
a. .8643
b. .7711
c. .1357
d. 4091
26. Which of the following is an example of a hypergeometric experiment?
a. Rolling a die 10 times and observing for a number
b. Finding the probability that a salesperson who sells .7 bedroom sets per day sells 3 today.
c. Tossing a coin 20 times and observing for a head or a tail
d. Drawing without replacement three yellow marbles from a box that contains 7 blue, and 11
yellow marbles.
27. Which of the following is not a condition to apply the Poisson probability distribution?
a. x is a discrete random variable
c. The occurrences are random
b. There are n identical occurrences
d. The occurrences are independent
28. For λ = 5.5, the probability of x = 2 is:
a. .0225
b. .0618
c. .0884
d. .1377
29. For λ = 4.2, the probability P(x < 2) is:
a. .1323
b. .2103
c. .0780
d. .8677
30. For λ = 3.4, the probability P(x > 7) is:
a. .0579
b. .0348
c. .9421
d. .0231
31. Each box of 100 bolts contains on average four defective bolts. The probability that a
randomly selected box of 100 bolts will contain exactly six defective bolts is:
a. .2615
b. .1042
c. .2319
d. .1824
32. An airline receives an average of 2.5 complaints per day. The probability that on a given day
this airline will receive no complaints is:
a. .1417
b. .0009
c. .2052
d. .0821
33. Each box of 500 light bulbs contains on average seven defective bulbs. The mean number of
defective light bulbs is:
a. 7
b. 2.646
c. 49
d. .4182
34. Each box of 500 light bulbs contains on average seven defective bulbs. The standard
deviation of defective light bulbs is:
a. 7
b. 2.646
c. 49
d. .4182
35. Which of the following is an example of a Poisson experiment?
a. Rolling a die 10 times and observing for a number
b. Finding the probability that a salesperson who sells .7 bedroom sets per day sells 3 today.
c. Tossing a coin 20 times and observing for a head or a tail
d. Drawing without replacement three yellow marbles from a box that contains 7 blue, and 11
yellow marbles.
CHAPTER 5 TEST
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