Question

Do you have enough “good cholesterol?” High-density lipoprotein (HDL) is sometimes called the “good cholesterol” because low values are associated with a higher risk of heart disease. According to the American Heart Association, people over the age of 20 years should have at least 40 milligrams per deciliter (mg/dl) of HDL cholesterol.40U.S. women aged 20 and over have a mean HDL of 55 mg/dl with a standard deviation of 15.5 mg/dl. Assume that the distribution is Normal.  

PLEASE SHOW YOUR ANSWER.

(a) What percent of women have low values of HDL (40 mg/dl or less)?

(b) HDL levels of 60 mg/dl and higher are believed to protect people from heart disease. What percent of women have protective levels of HDL?

(c) Women with more than 40 mg/dl but less than 60 mg/dl of HDL are in the intermediate range, neither very good or very bad. What proportion are in this category?

Answer 1

ANSWER:

High-density lipoprotein (HDL) is sometimes called the "good cholesterol" because low values are associated with a higher risk of heart disease.

For normal distribution

mean = 55 mg/dl

standard deviation = 15.5 mg/dl

(a)

What percent of women have low values of HDL.

40 mg/dl standardizes to

using table A 16.60% of women tall below this level.

(b)

What percent of women have protective levels of HDL.?

60 mg/dl standardizes to

37.45% if women have protective levels of HDL.

(c)

What proportion are in this category?

By substracting answer above 100%

We get 45.95%.

So nearly 46% of women tall in intermediate age.