The distribution of heights of young women aged 18 to 24 is approximately normal with a mean of 64.5 inches and a standard deviation of 2.5 inches. Between what

Question

two heights do the middle 95% of women fall

Answer 1

Using the empirical rule of 68%,95%, 99.7%

95% of the heights will be between ± 2 standard deviations of the mean

 

Mean = 64.5 inches

Standard Deviation = 2.5 inches

2 standard deviations = 2*2.5 = 5 inches

 

Mean less 2 standard deviations = 64.5 - 5 =59.5

Mean plus 2 standard deviations = 64.5 + 5 =69.5

 

95% fall between 59.5 and 69.5

Answer 2

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.

 

This says that approximately 95% of those observations fall within:

       64.5 - 2(2.5)  and  64.5 + 2(2.5)

  or

       64.5 - 5.0   and 64.5 + 5.0

        59.5 inches and 69.5 inches

 

[Note:  Memorize this rule!]