One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpets, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. Last year, there were 30 complaints concerning carpet installation. The following data represent the number of days between the receipt of a complaint and the resolution of the complaint:

54 5 35 137 31 27 152 2 123 81 74 27 11 19 126

110 110 29 61 35 94 31 26 5 12 4 165 32 29 28

Construct a 95% confidence interval estimate of the mean number of days between the receipt of a complaint and the resolution of the complaint.

You can use Excel to calculate the std and mean of the sample, but please use a calculator and tables for the rest of your answer. Please submit all of your calculations, Excel printouts, and the final answer. Please justify all steps of your solution.