A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made of a 14- gauge steel coil. It is produced using a 250- ton progressive punch press with a wipe- down operation and two 90- degree forms placed 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. Data are collected from a sample of 49 troughs and stored in Trough, which contains these widths of the troughs, in inches:

a. Compute the mean, median, range, and standard deviation for the width. Interpret these measures of central tendency and variability.

b. List the five- number summary.

c. Construct a boxplot and describe its shape.

d. What can you conclude about the number of troughs that will meet the company’s requirement of troughs being between 8.31 and 8.61 inches wide?

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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 8414 8481 8415 8.479 8.429 8.458 8.462 8.460 8.444 8.429 8460 8.412 8.420 8.410 8.405 8.323 8.420 8.396 8.447 8.405 8439 8411 8.427 8.420 8.498 8.409