Question

The distribution of heights of women aged 20 to 29 is approximately Normal with mean 65.4 inches and standard deviation 3.6 inches.

The height (± 0.1 inch) of the middle 99.7% of young women falls between a low of    inches and a high of   inches.

Answer 1

The 68-95-99.7 Rule
For Normal Distributions:

  Approximately 68% of the observations fall within 1 standard deviation of the mean.

  Approximately 95% of the observations fall within 2 standard deviations of the mean.

  Approximately 99.7% of the observations fall within 3 standard deviations of the mean.

Mean = 65.4 inches

Standard Deviation = 3.6 inches

3 standard deviations = 3*3.6 = 10.8 inches

Mean less 3 standard deviations = 65.4 - 10.8 =54.6

Mean plus 3 standard deviations = 65.4 + 10.8 =76.2

99.7% of young women falls between a low of 54.6 inches and a high of 76.2 inches.