Question: In most cities a municipal agency regulates the amounts charged by taxis. Total taxi fares are determined by distance traveled as well as the amount of time taken for the trip. In preparing to apply for a rate increase, the general manager of a taxi fleet wanted to know the distance customers travel by taxis on the average trip. She organized a survey wherein she asked taxi drivers to record the number of miles traveled by randomly selected customers. A sample of size 41 yielded the results below. The general manager wants to estimate the mean distance traveled with 95% confidence by using this sample. Find that estimate and state what assumptions must be satisfied for your estimate to be believable.

8.2 9.1 11.2 5.0 6.4 9.5 10.1 7.9 8.3 6.8 6.9 7.9 1.1 6.7 11.4 6.9 6.5 8.0 1.5 8.2 7.6 14.1 7.0 10.0 7.1 8.0 8.1 4.4 5.9 2.3 13.3 9.2 2.8 13.0 8.3 10.4 9.0 3.5 9.8 6.5 7.7