If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men? Assume the heights of American men are approximately Normally distributed.
A) 1 inch
B) 3 inches
C) 4 inches
D) 6 inches
E) 12 inches

Question

Quizplus · Accepted Answer

Assuming normal distribution, we know that 99.7% of values fall within 3 standard deviations (i.e., plus and minus) of the mean. Therefore, we can estimate the range of heights from:

Mean height +/- 3 * Standard deviation

Since the range of heights given (5'0" to 7'0") spans 24 inches, we can set up the following equation:

7*12 - 5*12 = 24 = 6*sigma

Thus, the estimated standard deviation would be 4 inches (i.e., 6/3). Option C is the closest choice to this estimation.

If the Heights of 99