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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.