Self-Assessment D
Probability Distributions
Name: _______________________________
1. Match the column on the left with the appropriate response on the right.
________ 1. Parameter of the Poisson distribution
a) 0
________ 2. Parameter of the Geometric distribution
b) 1
________ 3. Parameters of a normal distribution
c) p
________ 4. Parameters of the binomial distribution
d) 
_________5. Expected value of a binomial distribution
e) npq
_________6. Variance of a binomial distribution
f)  0.5
_________7. Mean of the standard normal distribution
g) n, p
_________8. Variance of the standard normal distribution h)  , 
_________9. probability of failure
_________10. Continuity correction factor for the normal
approximation to the binomial
i) np
j) q
2. Suppose it is know that 10% of the students in a Statistics course fail the final exam. What is
the probability that in a class of 30 students
a) Exactly 4 of them will fail the final exam?
a)
b) At least 80% of the class (that is, at least 24 of the students)
will pass the final exam?
b)
c) At most 4 of them will fail the final exam?
c)
d) How many of the students in the class do you expect will
pass the final exam?
d)
e) What is the standard deviation for the distribution of students
who fail the final exam?
e)
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3. A factory production inspector expects an average of 5.2 defective items on a given day’s
production. What is the probability that
a) on a given day he will find only 4 defective items?
a)
b) on a given day he will find less than 8 defective items
b)
c) on a given week (5 days of work) he will find more than 30
defective items
c)
4. The probability that a person will want to take a room at a certain motel is 0.3.
What is the probability that
a) The first room is rented to the fifth person who inquires
a)
b) The first room is rented before the fifth person inquires?
b)
5. In a binomial problem n=10000 and p=0.005). Find the approximate probability
of obtaining 40 successes.
answer: ____________
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6. For the standard normal distribution, find
a) the probability that a vale falls between -1.96 and 1.65
a)
b) the value that corresponds to the 90th percentile
b)
c the value that corresponds to the 1st quartile.
c)
d) the ordinate (the y-value) which corresponds to z=1.28
d)
7. The average rent for a two bedroom apartment in Bolivar City is $950 with a standard
deviation of $125. If the distribution of rental prices for a two bedroom apartment in Bolivar City
is approximately normal, find
a) The probability that a person will find a two bedroom
apartment for less than $780 in Bolivar City.
a)
b) The percentage of two bedroom apartments in Bolivar City
that are rented for $1200 or more.
b)
c) The rental cost for two bedroom apartments at Bolivar City
above which we find the most expensive 40% of the apartment.
c)
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8. The amount of coffee dispensed by a certain coffee machines is normally distributed with an
average of 6 ounces per cup and a standard deviation of 0.6 ounces.
a) What is the probability that a given person will get less than 5.5
ounces of coffee?
a)
b) What is the probability that a 7-ounce cup will overflow?
b)
c) 80% of the time the coffee machine will dispense an amount of
coffee which is more than 5 ounces but less than what number?
c)
d) A company inspector only wants 10% of the customers to receive
less than 5.5 ounces. What should the mean be set at?
d)
e) In part d) instead of changing the mean, what standard deviation is
needed to achieve the same result?
e)
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9. In a binomial problem n=400 and p=0.9.
a) Find the mean
a)
b) Find the standard deviation
b)
c) Find the probability of anywhere from 350 to 365 successes.
c)
d) Use the normal approximation to the binomial with the
 0.5 continuity correction factor to find the probability of anywhere
from 350 to 365 successes.
d)
10. In a bowl there 15 red balls and 12 blue balls. If 9 balls are selected at random, what is the
probability that there will be 3 red balls and 6 blue balls?
10. ____________
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Answers:
1. d-1
c-2
h-3 g -4
i-5
e-6 a-7
b-8
2. a) binomial pdf (30, .10, 4) =0.1770659492
b) 1 – binomial cdf (30, .90, 23) = 0.9741732113
c) binomial cdf (30, .10, 4) = 0.8245051191
d)   np  30(.90)  27
i-9
f-10
e)   npq  30(.10)(.90)  1.643167673
3. a) Poisson pdf (5.2, 4) = 0.1680625028
b) Poisson cdf (5.2, 7) = 0.8449215903
c) 1 – Poisson cdf (26, 30) = 0.1865525718 Note: if the expected number is   5.2
defective items per day, then   5(5.2)=26 defective items per week (5 working days
in a week)
4. a) geometpdf ( 0.3, 5) = 0.07203
b) geometcdf (0.3, 4) =0.7599
5. Using the Poisson approximation to the binomial with   np =10000(0.005) =50 we obtain:
Poisson pdf( 50, 40) =0.0214996312
6. a) normalcdf (-1.96, 1.65) = 0.925530724
b) invNorm (0.90) =1.281551567
c) invNorm (0.25) = -0.6744897495
d) normalpdf (1.28) =0.1758474303
7. a) normalcdf ( -10^9, 780, 950, 125) = 0.0869150207
b) normalcdf ( 1200, 10^9, 950, 125) = 0.022750062
c) invNorm (0.60, 950, 125) = $981.67
8. a) normalcdf(-10^9, 5.5, 6, 0.6) = 0.2023283246
b) normalcdf(7, 10^9, 6, 0.6) =0.0477903304
c) eq: 0= normalcdf(5, x, 6, .6) – 0.80
ALPHA SOLVE answer: 6.6162014739 ounces.
d) eq: 0= normalcdf(-10^9, 5.5, x, .6) – 0.10
ALPHA SOLVE answer: 6.2689311632 ounces.
e) eq: 0= normalcdf(-10^9, 5.5, 6, x) – 0.10
ALPHA SOLVE answer: 0.39015195944 ounces
9. a)   np  400(.9)  360
b)   npq  400(.9)(.1)  6
c) binomcdf(400, .9, 365) – binomcdf(400, .9, 349) = 0.7758791727
d) normalcdf(349.5, 365.5, 360, 6) =0.7802822448
10. Hypergeometric
15 12 
  
3 6
455  924
P(3 red and 6 blue)     
 0.897026129
4686825
 27 
 
9 
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