Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year.
a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between 6 and 7 pairs of sports shoes?
c. What is the probability that the difference between the sample mean and the population mean is less than 0.25 pair?
d. What is the likelihood the sample mean is greater than 7 pairs?