A company produces steel housings. A main component is a steel trough made from

Question

A company produces steel housings. A main component is a steel trough made from a 14 gauge steel coil. It's produced using a 250 ion progressive punch press with a wipe-down operator that puts to 90 degree forms in the flat steel to mak the trough. The company requires the width of the trough be tween 8.31 inches and 8.610 inches The widths of the samples of 49 troughs are stored in the table below:

:8.312 8.393 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 8.405 8.323 8.420

8.409 8.447 8.405 8.439 8.411 8.427 8.420 8.498

a. Construct a frequency distribution and percentage distribution.

b. Construct a cumulative percentage distribution.

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

Explanation / Answer

(a) Here N=49:

Following is the frequency and percentage distribution :

(b) Following is the cummulative frequency distribution:

Cummulative percenatges:

For second row : 6.12%+6.12%=12.24%

For third row: 12.24%+10.20%=22.45%

(c)

In the sample, all 100% troughs are between 8.31 and 8.61.

Interval Frequency (f) Percentage (%) =((f/N)*100) 8.312-8.343 3 6.12 8.343-8.374 3 6.12 8.374-8.405 5 10.20 8.405-8.436 13 26.53 8.436-8.467 17 34.69 8.467-8.498 8 16.33 Total 49 100

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