Aontario 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 be between 8.31 inches and 8.61 inches. the widths of the troughs, in inches, are collected from a sample of 49 troughs and stored in trough and shown here:

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 8.415 8.479 8.429 8.458 8.462 8.460 8.444
8.429 8.460 8.412 8.420 8.410 8.405 8.323 8.420
8.396 8.447 8.405 8.439 8.411 8.427 8.420 8.498
8.409

a. construct a frequency distribution and a percentage distribution.
b. construct a cumulative percentage distribution.
c. what can you conclude about the number of troughs that will meet the company’s requirements of troughs being between 8.31 and 8.61 inches wide?