The local regional transit authority of a large city was interested in determining the mean

commuting time for workers who drive to work. They selected a random sample of 125

workers who drive to work and asked them how long they spent commuting to work (in

minutes). A 95% confidence interval was constructed and reported as (27.74, 30.06).

(a) Show that the conditions for calculating a confidence interval for a mean are satisfied.

(b) Interpret the interval in the context of this problem.