The serum total cholesterol for males 20 to 29 years old is

The serum total cholesterol for males 20 to 29 years old is approximately normally distributed with mean 180 and standard deviation 36.2, based on data obtained from the National Health and Nutrition Examination Survey. Use the 68-95-99.7 rule to determine:

a) The middle 68% of values. What percent of values fall below this range? What percent fall above this range?

b) What range of values will capture the middle 95%

Standardizing a normal random variable: Find the Z-score of any particular value

c) What is a z score for a serum total cholesterol level of 170?

d) What is a z score for a serum total cholesterol level of 190?

A continuous random variable, x, is normally distributed with a mean of 200 grams and a standard deviation of 25 grams. Convert each of the following x values into its corresponding z-scores:

a. x= 150

b. x= 200

c. x= 315

d. x= 180

e. x= 285

Solution

a) The middle 68% of values.

= (180 + / - 36.20)

= 143.8 to 216.2 are middle 68 percent of the values.

What percent of values fall below this range?

= (100 - 68 ) / 2

= 34 /2

= 17%

What percent fall above this range?

= (100 - 68 ) / 2

= 34 /2

= 17%

Middle 95% of the values are:

= 180 +/- (2*36.2)

= 180 +/- 72.4

= (107.6, 252.4)

b) Z-score = X - mean / S.D