Too much cholesterol in the blood increases the risk of heart disease. Young wom
ID: 3241391 • Letter: T
Question
Too much cholesterol in the blood increases the risk of heart disease. Young women are generally less afflicted with high cholesterol than other groups. The cholesterol levels for women aged 20 to 34 follow an approximately Normal distribution with mean 170 milligrams per deciliter (mg/dl) and standard deviation 40 mg/dl. Please use 4 decimal places to answer the following questions.
(a) Cholesterol levels above 240 mg/dl demand medical attention. What proportion of young women have levels above 240 mg/dl?
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(b) Levels above 200 mg/dl are considered elevated and place the person at some risk of cardiovascular disease. What proportion of young women have blood cholesterol between 200 and 240 mg/dl?
________
Middle-aged men are more susceptible to high cholesterol than the young women of the previous exercise. The blood cholesterol levels of men aged 55 to 64 are approximately Normal with mean 221 mg/dl and standard deviation 41 mg/dl. Please use 4 decimal places to answer the following questions.
(c) What proportion of these men have high cholesterol (levels above 240 mg/dl)?
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(d) What proportion have elevated cholesterol (between 200 and 240 mg/dl)?
________
Explanation / Answer
1. mean = 170, s = 40
a) P(X > 240) = 1 - P(X < 240) = 1 - P(Z < (x-mean)/s) = 1 - P(Z < (240-170)/40) = 1 - P(Z < 1.75) = 0.0401 = 0.04
b) P(200 < X < 240) = P(X < 240) - P(X < 200) = P(Z < (240-170)/40) - P(Z < (200-170)/40) = P(Z < 1.75) - P(Z < 0.75)
= 0.9599 - 0.7734 = 0.1865 = 0.19
c) P(X > 240) = 1 - P(X < 240) = 1 - P(Z < (x-mean)/s) = 1 - P(Z < (240-221)/41) = 1 - P(Z < 0.46341) = 0.3215
= 0.32
d) P(200 < X < 240) = P(X < 240) - P(X < 200) = P(Z < (240-221)/41) - P(Z < (200-221)/41) = P(Z < 0.46341) - P(Z < -0.51220)
= 0.6785 - 0.3043 = 0.3742 = 0.37