The serum total cholesterol for males 20–29 years old is approximately normally distributed with mean μ = 180 and σ = 36.2, based on data obtained from the National Health and Nutrition Examination Survey.

(a) Draw a normal curve with the parameters labeled.

(b) An individual with total cholesterol greater than 200 is considered to have high cholesterol. Shade the region under the normal curve to the right of x = 200.

(c) Suppose that the area under the normal curve to the right of x = 200 is 0.2903. Provide two interpretations of this result.

Approach

(a) Draw the normal curve with the mean μ = 180 labeled at the high point and the inflection points at μ – σ = 180 - 36.2 = 143.8 and μ + σ = 180 + 36.2 = 216.2.

(b) Shade the region under the normal curve to the right of x = 200.

(c) The two interpretations of the area under a normal curve are 

(1) a proportion

(2) a probability.