**Estimation of Height Distribution**

Use the results of Example 7.2-1 to estimate how many 20-year-old men are no taller than 68 in. How many are within 3 in. of the mean?

**Solution**

In Example 7.2-1 the mean and standard deviation were found to be J-L = 69.3 in. and (1= 1.96 in. In Table. 7.2-1, note that few data points are available for heights less than 68 in. However, if yo.p assume that the heights are normally distributed, you can use equation (7.2-4) to estimate how many men are shorter than 68 in. Use (7.2-4) with b = 68 that is;

To determine how many men are within 3 in. of the mean, use (7.2-5) with a = π – 3 = 66.3 and b = π +3 = 72.3; that is,

In MATLAB these expressions are computed in a script file as follows:

When you run this program, you obtain the results P 1 = O. 2 5 3 6 and P2 = O. 8741. Thus 25 percent of 20-year-old men are estimated to be 68 inches or less in eight, and 87 percent are estimated to be between 66.3 and 72.3 inches tall.

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