3.64. 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. Dataare collected from a sample of 49 troughs and stored in Trough, which contains the widths of the troughs in inches as shown below.

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. Calculate the mean, median, rangeand standard deviationfor the width. Interpret these measures of central tendencyand variability.

b. List the five-number summary.

c. Construct a box plotand 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?

3.65. The manufacturing company in Problem 3.64 also produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to an insulator before it breaks. Data are collected from a sample of 30 insulators. The file Force contains the strengths as follows:

1870 1728 1656 1610 1634 1784 1522 1696 1592 1662 1866 1764

1734 1662 1734 1774 1550 1756 1762 1866 1820 1744 1788 1688

1810 1752 1680 1810 1652 1736

a. Calculate the mean, median, range and standard deviation for the force needed to break the insulator.

b. Interpret these measures of central tendency and variability in (a).

c. Construct a box plot and describe its shape.

d. What can you conclude about the strength of the insulators if the company requires a force measurement of at least 1500 pounds before breakage?

The solution provides step by step method for the calculation of descriptive statistics. Formula for the calculation and Interpretations of the results are also included.