A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made out of 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 weatherproofing in outdoor applications. The company requires that the width of the trough must be between 8.31 inches and 8.61 inches. In the past, the standard deviation of the width of the trough has been 0.05 inch. The file Trough 2 contains the widths of the troughs, in inches, for a sample of $n=25$ :
$$
\begin{array}{lllllllll}
8.312 & 8.343 & 8.317 & 8.383 & 8.348 & 8.410 & 8.351 & 8.373 & 8.481 \\
8.422 & 8.476 & 8.382 & 8.484 & 8.403 & 8.414 & 8.419 & 8.385 & 8.465 \\
8.498 & 8.447 & 8.436 & 8.413 & 8.489 & 8.414 & 8.481 & &
\end{array}
$$b. What assumption about the population distribution is needed in order to conduct the test in (a)?