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Chapter 2: Q T2.7. (page 149)

If the heights of a population of men are approximately Normally distributed, and the middle 99.7%have heights between 5′0″and 7′0″what is the standard deviation of the heights in this population?

a.1″b.3″c.4″d.6″e.12″

Short Answer

Expert verified

The correct option is c. 4″

Step by step solution

01

Given information

99.7%of the height is between 5’0’’and7’0’’

02

Calculation

The normal distribution rule states that 99.7% of data will fall within three standard deviations of the mean.

The mean is 6'0" since it is at the midpoint of the interval.

Also, 3 standard deviation is between 5'0" and 6'0" tall.

3σ=1'0''=12''

Dividing each side by 3:

σ=12'4=4''

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