Project: Normal (Stat)

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

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

Female Data in inches

66.4	68.1	66.7	67.9	63.1	67.8	66.1	68.9
66.1	69.2	64.9	67.6	57.6	65.1	66.7	67.8
66.8	63.6	67.5	60.2	69.4	68.4	62.2	67.2
64.7	66.3	64.2	62.2	64.3	67.2	63.2	58.1

A. Use the TI-83 / 84 to get a Normal Probability Plot to verify that the data is Normally distributed.
Does the data appear to be linear?

    B. Use STAT to find the sample mean and sample standard deviation for the data. (Round to tenths.)
          1. Mean                       2. Standard deviation
          Use these statistics (sample mean and sample standard deviation) as point estimates for the population
           parameters (population mean and population standard deviation).

    C. Use the Normal Probability Distribution table or the built-in functions of your calculator to 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?

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

Male Data in inches

68	65.5	68.1	72.5	65.4	71.2	67.7	73.5
67.7	65.1	65.3	65.5	72	73.2	62.5	77.2
70.5	66.7	67.5	70.2	67.4	71.8	65.1	67.2
66.3	69.3	67.7	67	73.8	66.5	66.1	68.6

A. Use the TI-83 / 84 to get a Normal Probability Plot to verify that the data is Normally distributed.
Does the data appear to be linear?

    B. Use STAT 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 for the population
          parameters (population mean and population standard deviation).

     C. Use the Normal Probability Distribution table or the built-in functions of your calculator to 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?

     D. Because of the high cost of leather, the company has decided they cannot profitably make leather pants in all sizes.
           Use the Normal Probability Distribution table or the built-in functions of your calculator to find the heights
           corresponding to the following percentages. These are the heights of the shortest and tallest 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.