Percentage of 10th grade boys

Question

Suppose that the mean height of 10th grade boys is 69 inches with a standard deviation of 2 inches and that it follows a Normal distribution. Using the empirical rule, determine the percentage of 10th grade boys below 67 inches

Answer 1

mean =69

standard deviation =2

Test point X=67

 

Z-Score= (X-mean)/Standard deviation

Z-Score= (67-69)/2 = -2/2=-1

68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.

 

so the the percentage of 10th grade boys below 67 inches will be (100%-68%)/2= 16%

 

Answer is 16%