Name: _____________________________________________
Sampling Distributions and Central Limit Theorem Review
This is not a complete review – be sure to look over the sampling distributions quiz since this
review does not include any problems on the following topics:
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sampling distributions vs. population distributions (see last question on the quiz)
unbiased estimator
sampling variability (how to reduce this)
statistic vs. parameter
1. Suppose that in the large population of able-bodied college men the time to run a mile has
mean 7.11 minutes and standard deviation of 0.739 minutes. Suppose these times have a normal
distribution.
a) What is the probability that a randomly chosen man runs the mile in 7 minutes or less?
b) Next, choose a random sample of 20 college men. What is the probability that their average
time for the mile is 7 minutes or less?
2. Yoonie is a personal manager in a large corporation and must review employees. Suppose
that the time it takes to do a review has a mean of 4 hours with a population standard deviation
of 1.2 hours. This month she must review 40 of the employees. What is the probability that the
average time it will take her to complete the 40 reviews is more than 4.25 hours?
3. The time it takes students in a cooking school to learn to prepare seafood gumbo has a mean
of 3.2 hours with a standard deviation of 1.8 hours.
a) Find the probability that it will take a class of 36 students to learn to prepare seafood gumbo
is less than 3.4 hours.
b) Find the probability that it takes one student between 3 and 4 hours to learn to prepare
seafood gumbo.
4. A soft-drink machine is regulated so that it discharges an average of 200 milliliters per cup of
soda. The amount of drink is normally distributed with a standard deviation equal to 15
milliliters.
a) What is the probability that a sample of 5 cups of soda will have more than 210 milliliters?
b) 84% of sample means from 5 cups of soda hold less than how many average milliliters?
5. You are the director of transportation safety for the state of Georgia. You are concerned
because the average highway speed of all trucks may exceed the 60 mph speed limit. You take a
random sample of 120 trucks. Assume the population mean is 60 mph and population standard
deviation is 12.5 mph.
a) Find the probability that the average speed is greater than or equal to 62 mph.
b) 20% of the average speeds from samples of size 120 are greater than what average speed?
6. You work at a bakery and your boss has determined that the cooking time for a new kind of
muffin is slightly skewed right with a mean of 8 minutes and a standard deviation of 2 minutes.
a) What is the probability that a muffin will take longer than 9 minutes to cook?
b) For a sample of 4 muffins, what is the probability that the average cooking time will exceed 9
minutes?
c) For a sample of 34 muffins, what is the probability that the average cooking time will exceed 9
minutes?
7. A biologist find that the lengths of adult fish in a species of fish she is studying follow a normal
distribution with a mean of 10 inches and a standard deviation of 2 inches.
a) Find the probability that an individual adult fish is between 9.5 and 10.5 inches long.
b) Find the probability that for a sample of 16 adult fish, the average length is between 9.5 and
10.5 inches.
c) Find the probability that for a sample of 25 adult fish, the average length is between 9.5 and
10.5 inches.
d) Find the probability that for a sample of 64 adult fish, the average length is between 9.5 and
10.5 inches.
8. Suppose that the length of time that a student waits for help in the math lunch lab during the
first week of school has a skewed distribution with a mean of 5 minutes and a standard deviation
of 2.3 minutes.
a) Find the probability that an individual student waits between 4 and 6 minutes.
b) Find the probability that for a sample of 35 students the average wait is between 4 and 6
minutes.
9. The weights of packages shipped by an air express company follow an unknown distribution
with an average of 13.5 pounds and a standard deviation of 8 pounds. Find the probability that
for a randomly selected sample of 49 packages, the average weight is between 13 and 14 pounds.