1)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 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 a flat steel to make the trough. The company requires that the width of the trough be between 8.31 inches and 8.43 inches. Data are collected from a sample of 49 troughs.

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, percentage distribution, cumulative frequency, and a cumulative percentage distribution.

Class Interval Frequency Percentage Cumulative Frequency Cumulative Percentage

b) Construct a frequency distribution histogram, a cumulative frequency histogram, a cumulative percentage polygon plot and a percentage distribution pie chart using excel.

Paste charts from Excel below:

c) What can you conclude about the number of trough that will meet the company’s requirements of troughs being between 8.31 and 8.43 inches wide?

2)If the data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the corresponding z-score to the time of 4.0 seconds?

3)Suppose 95% of the data falls between 12.4 and 46.8 units. Using the empirical rule, give an estimate of the standard deviation.

4)Make a stem and leaf plot of the data, what is the shape of the data

45, 111, 105, 50, 48, 77, 71, 51, 55, 92, 56, 57, 65, 62, 51, 68, 44, 68, 57, 62, 91, 57

Insert stem and leaf plot below:

5)Use the 22 average daily temperatures and the 22 corresponding 22 amounts of energy consumption (kWh) to construct a scatter plot in Excel. Based on the graph, is there a relationship between the 2 variables? Identify at least one reason as to why there is or isn’t a relationship.

Average Daily Temp. kWh

29 3637

37 2888

57 2359

74 3704

66 3432

47 2446

28 4463

41 2482

54 2762

68 2288

62 2423

42 3375

26 2661

34 2073

58 2579

72 2858

67 2296

48 2812

33 2433

39 2266

66 3128

71 3286

Paste charts from Excel below:

6)The following data contains the overall miles per gallon of 2009 sedans priced under $20,000.

27 31 30 28 27 24 29 32 31 27 26 25 26 25 24

a) Compute the mean, median, mode, variance, standard deviation, range, and coefficient of variation, Q1 (Quartile 1) and Q3 (Quartile 3) using Excel.

Cut and paste cells from Excel below:

b) What is the shape of the data? How do you know?