Runners in a race have a mean finishing time of 91 minutes and a standard deviation of 16 minutes. If we assume the runner’s times are normally distributed, answer the following: a) What is the probability that the finishing time of a single randomly selected runner is within 5 minutes of the population mean? b) What is the probability that the sample mean finishing time of 9 runners is within 5 minutes of the population mean? c) What is the probability that the sample mean finishing time of 49 runners is within 5 minutes of the population mean? d) Compare the probabilities. What does this tell us about the benefits of a large sample size for estimating the population mean?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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) Runners in a race have a mean finishing time of 91 minutes and a standard deviation of 16 minutes. If
we assume the runner’s times are normally distributed, answer the following:
a) What is the probability that the finishing time of a single randomly selected runner is within 5 minutes
of the population mean?
b) What is the probability that the sample mean finishing time of 9 runners is within 5 minutes of the
population mean?
c) What is the probability that the sample mean finishing time of 49 runners is within 5 minutes of the
population mean?
d) Compare the probabilities. What does this tell us about the benefits of a large sample size for
estimating the population mean?

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