Chapter 2.2, Problem 43E

(a)

To determine

To find: the percent of men who are taller than 74 inches

Answer to Problem 43E

Approximately 2.5 % of men are taller than 74 inches.

Explanation of Solution

Calculation:

The distribution of heights is approximately N (69, 2.5). Figure below is a sketch of the Normaldensity curve with the desired points labeled.

  

By the 68-95-99.7 rule, approximately 2.5% of men are taller than 74 inches, which is 2standard deviations above the mean.

  

Conclusion:

Therefore,2.5% of men are taller than 74 inches

(b)

To determine

To find: the height range where the middle 95% of men fall

Answer to Problem 43E

Approximately 95% of men have heights between 64 inches and 74 inches.

Explanation of Solution

Calculation:

By the 68-95-99.7 rule, approximately 95% of men have heights between 64 inches and 74inches which fall within 2s of µ.

  

Conclusion:

Therefore, 95% of men have heights between 64 inches and 74inches

(c)

To determine

To find: the percent of men who arebetween 64 and 66.5 inches tall

Answer to Problem 43E

Approximately16% -2.5% = 13.5% of men have heights between 64 inches and 66.5 inches.

Explanation of Solution

Calculation:

By the 68-95-99.7 rule, approximately 16% of men are shorter than 66.5 inches, because66.5 is one standard deviation below the mean. Approximately 2.5% are shorter than 64 inches,because 64 inches is two standard deviations below the mean. So approximately 16% - 2.5% = 13.5% of men have heights between 64 inches and 66.5 inches.

Conclusion:

Therefore, 16% -2.5% = 13.5% of men have heights between 64 inches and 66.5 inches.

(d)

To determine

To find: the percentile of adult male American heights corresponding to 71.5 inches height.

Answer to Problem 43E

Here, 71.5 is the 84^th percentile of adult male American heights.

Explanation of Solution

Calculation:

By the 68-95-99 .7 rule, the value 71.5 is one standard deviation above the mean. Thus, the area to the left of 71.5is 0.68 +0.16 = 0.84. In other words, 71.5 is the 84^th percentile of adult male American heights.

  

Conclusion:

Therefore, 71.5 is the 84^th percentile of adult male American heights.