Question

High-density lipoprotein (HDL) is sometimes called the "good cholesterol" because high values are associated with a lower risk of heart disease. According to the American Heart Association, people over the age of 20 years should have at least 40 mg/dL of HDL cholesterol. U.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.

Women with more than 40 mg / dL but less than 60 mg / dL of HDL are in the intermediateWomen 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?range neither very good or very bad. What proportion are in this category?

(Fill in the blank below and round your answer to a whole number.)

% of women are in the intermediate range

Answer 1

Solution:

We are given that the variable follows normal distribution.

µ = 55

σ = 15.5

We have to find P(40<X<60)

P(40<X<60) = P(X<60) – P(X<40)

First find P(X<60)

Z = (X - µ)/σ

Z = (60 - 55)/15.5

Z = 0.322581

P(Z<0.322581) = P(X<60) = 0.626494

(by using z-table or excel)

Now find P(X<40)

Z = (X - µ)/σ

Z = (40 - 55)/15.5

Z = -0.96774

P(Z<-0.96774) = P(X<40) = 0.166587

(by using z-table or excel)

P(40<X<60) = P(X<60) – P(X<40)

P(40<X<60) = 0.626494 - 0.166587

P(40<X<60) = 0.459907

Required probability = 0.459907 ≈ 46%

46% of women are in the intermediate range.