The 68-95-99.7 Rule

Question

Consider that the National Health Center for Statistics reports that females (age 21) have heights that are normally distributed, approximately centered at a mean of 65 inches (5 feet 5 inches) with a standard deviation of 2.5 inches. Use the 68-95-99.7 Rule to find the percentage of females (age 21) with heights in each of the following scenarios:
 

Percentage of heights greater than 67.5:  ?%


Percentage of heights less than 70: ?%
 

Percentage of heights between 62.5 and 65: ?%
 
 
Percentage of heights between 62.5 and 70:  ?%
 

Answer 1

Hi Marian,

 

This picture should help you visualize the question.

 

http://img.tfd.com/mk/D/X2604-D-41.png

 

Percentage of heights greater than 67.5: This is asking for everything higher than 67.5, or 1 standard deviation (SD) above the mean, which is 16%

 

Percentage of heights less than 70: This is asking for everything less than 70, or 2 SD above the mean, which is 100%-2.5%, or 97.5%

 

Percentage of heights between 62.5 and 65: This is asking for everything higher than 62.5, or 1 SD below the mean, but less than the mean, which is 34%

 

Percentage of heights between 62.5 and 70: This is asking for everything higher than 62.5, or 1 SD below the mean, but less than 70, or 2 SD above the mean, which is 81.5%