Percentage

Question

The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. What percentage of teenage boys have levels between 170 and 225?

Answer 1

We want to find the P(170<x<225).

To do so we find the z scores associated with both 170 and 225.

 

z= (x-µ)/σ

 

z1= (170-170)/30 = 0

 

z2= (225-170)/30 = 1.833

 

Then, if you are using a graphing calculator, go to 2nd vars, number 2 and enter 

normalcdf(0,1.833) since 0 is the lowest z score included, and 1.833 is the highest z score included.

This yields .4665.

 

Alternatively, if you are using a z table, look up the probabilities associated with both z scores, and subtract the probability of a z score of 0 from the probability of a z score of 1.833 (you do this because the probability associated with each accounts for all z scores beneath it, so you would be accounting for z scores from negative infinity to 0 twice if you did not subtract). 

 

Either method will yield an answer of .4665, which when converted to a percentage is about 46.65%.