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 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weather proofing in outdoor applications. The widths (in inches), shown below and stored in trough, are from a sample of 49 troughs:

a. Constrict a 95% confidence interval estimate for the mean width of the troughs.

b. Interpret the interval develop in (a).

c. Do you think the assumption needed to construct the confidence interval estimate in (a) in valid?

8.312 8.422 8.498 8.429 8.410 8.427 8.343 8.476 8.447 8.458 8.405 8.420 8.317 8.382 8.836 8.462 8.323 8.498 8.383 8.484 8.413 8.460 8.420 8.409 8.348 8.403 8.489 8.444 8.396 8.410 8.414 8.414 8.429 8.447 8.351 8.419 8.481 8.460 8.405 8.373 8.385 8.415 8.412 8.439 8.481 8.465 8.479 8.420 8.411