Question

The distribution of heights of women aged 20 to 29 is approximately Normal with mean μ = 67.0 inches and standard deviation σ = 2.9 inches. (Enter your answers to one decimal place.)

The height of the middle 95% of young women falls between a low of ______inches and a high of_____ inches.

Answer 1

= 67.0

= 2.9

Middle 95% corresponds to area = 0.95/2 = 0.475 from mid value to Z on either side.

Table of Area Under Standard Normal Curve gives Z = 1.96

So,

low side:

67.0 - (1.96 X 2.9)

= 67.0 - 5.684

= 61.3

high side:

67.0 + (1.96 X 2.9)

= 67.0 + 5.684

= 72.7

So,

Answer is:

The height of the middle 95% of young women falls between a low of 61.3 inches and a high of 72.7 inches.