In the United States, the mean average height of adult women is approximately 65.5 inches, with a standard deviation of 2.5 inches.

Question

In the United States, the mean average height of adult women is approximately 65.5 inches, with a standard deviation of 2.5 inches. If height is normally distributed,what percent of the women in this country are between 63 and 70.5 inches tall?

Answer 1

Easiest way to find probability of women between 63 and 70.5 inches tall is to find probability < 70.5 and subtract the probability < 63

 

Easiest way to find probability of of 63 and 70.5 is to calculate z score of each

 

z score of 63 = (x-mean)/std = (63-65.5)/2.5 = -1 using a z table gives us prob < 63 is .1587

 

z score of 70.5 = (x-mean)/std = (70.5-65.5)/2.5 = 2 using a z table gives us prob < 70.5 is .9772

 

Subtract the .1587 from .9772 gives us .8185 or 81.85%