PROJECT: NORMAL PROBABILITY DISTRIBUTION

Objective: Use the Normal Probability Distribution to make decisions about apopulation.

Scenario: An apparel company makes blue jeans and leather pants.I. The female division.

Female Data in inches

66.4 68.1 66.7 67.9 63.1 67.8 66.1 68.966.1 69.2 64.9 67.6 57.6 65.1 66.7 67.866.8 63.6 67.5 60.2 69.4 68.4 62.2 67.264.7 66.3 64.2 62.2 64.3 67.2 63.2 58.1

A. Use the "Statistics" function of your calculator to find the sample mean and samplestandard deviation for the data. (Round to tenths.) 1. Mean 2. Standard deviation Use these statistics (sample mean and sample standard deviation) as point estimates forthe population parameters (population mean and population standard deviation) when calculating thestandard (z) scores.

B. Use the Normal Probability Distribution table or the built-in functions of your calculatorto find: 1. What percent of female adults are taller than 6 feet (72 inches)? 2. What percent of female adults are taller than 5 feet (60 inches)? 3. What percent of female adult heights are between 60 inches and 72 inches?

C. Because of the high cost of leather, the company has decided they cannot profitably makeleather pants in all sizes. Use the Normal Probability Distribution table or the built-in functions of your calculatorto find the heights corresponding to the following percentages. These are the heights of the shortest andtallest females who can purchase leather pants from this company. 1. The bottom 8% 2. The upper 6%

II. The male division

Male Data in inches

68 65.5 68.1 72.5 65.4 71.2 67.7 73.567.7 65.1 65.3 65.5 72 73.2 62.5 77.270.5 66.7 67.5 70.2 67.4 71.8 65.1 67.266.3 69.3 67.7 67 73.8 66.5 66.1 68.6

A. Use the "Statistics" function of your calculator to find the sample mean and sample

standard deviation for the data. (Round to hundredths.) 1. Mean 2. Standard deviation Use these statistics (sample mean and sample standard deviation) as point estimates forthe population parameters (population mean and population standard deviation) when calculating thestandard (z) scores.

B. Use the Normal Probability Distribution table or the built-in functions of your calculatorto find: 1. What percent of male adults are shorter than 6 feet (72 inches)? 2. What percent of male adults are shorter than 5 feet (60 inches)? 3. What percent of male adult heights are between 60 inches and 72 inches?

C. Because of the high cost of leather, the company has decided they cannot profitablymake leather pants in all sizes. Use the Normal Probability Distribution table or the built-in functions of yourcalculator to find the heights corresponding to the following percentages. These are the heights of the shortest andtallest males who can purchase leather pants from this company. 1. The bottom 9% 2. The upper 7%

Click on the hand to view the solutions using the Standard Normal Probability Table.

Select the TI-83 calculator to view how to use the built in NormalProbability programs:

"normalcdf(" and "invNorm("