A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made from a 14gauge steel coil. It is produced using a 250ton progressive punch press with a wipe-down operation that puts two 90degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weatherproofing in outdoor applications. The widths (in inches), shown below and stored in Through are from a sample of 49 through:

a. Construct a 95% confidence interval estimate for the mean width of the troughs.
b. Interpret the interval developed in (a).
c. Do you think the assumption needed to construct the confidence interval estimate in (a) in valid?