The Bendbo Corporation has a total of 300 employees in its two manufacturing locations and the headquarters office. A study conducted five years ago showed the average commuting distance to work for Bendbo employees was 6.2 miles with a standard deviation of 3 miles. Recently, a follow-up study based on a random sample of 100 employees indicated an average travel distance of 5.9 miles.
a. Assuming that the mean and standard deviation of the original study hold, what is the probability of obtaining a sample mean of 5.9 miles or less?
b. Based on this probability, do you think the average travel distance may have decreased?
c. A second random sample of 40 was selected. This sample produced a mean travel distance of 5.9 miles. If the mean for all employees is 6.2 miles and the standard deviation is 3 miles, what is the probability of observing a sample mean of 5.9 miles or less?
d. Discuss why the probabilities differ even though the sample results were the same in each case.