Download Module 24: Sampling Distributions and the Central Limit Theorem

Module 24: Sampling Distributions and the Central Limit Theorem: DIY
DIY: The per capita consumption of coffee by people in the United States in a recent year was normally
distributed, with a mean of 24.2 gallons and a standard deviation of 8.1 gallons. Random samples of 30 are
drawn from this population and the mean of each sample is determined. Find the mean and standard error
of the mean of this sampling distribution.
DIY: The mean height of men in the United States (ages 20-29) is 69.9 inches with a standard deviation of
3.0 inches. A random sample of 60 men in this age group is selected. What is the probability that the mean
height for the sample is greater than 70 inches?
About 40% of samples of 60 men will
have a mean greater than 70 inches.
DIY: A manufacturer claims that the life span of its tires is 50,000 miles with a standard deviation of 800
miles. You work for a consumer protection agency and you are testing this manufacturer’s tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The
mean life span is 49,721 miles.
Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 49,721 miles or less?
Using your answer, what do you think of the manufacturer's claim?
The sample mean of 100 tires was 49,721 which resulted in a zscore of -3.49 which would be very unlikely to happen if the claim
was true. Based on this data, the claim in not truthful.
Would it be unusual to have an individual tire with a life span of 49,721 miles? Why or
why not?
Assuming the claim is true, it would not be unusual for an individual tire to have that type of life span since its
z-score is within one standard deviation from the mean. This is different from the one above because we are
talking about one tire not a group of 100 tires.