\"Good\" cholesterol (known as \"HDL\") is protective against heart disease. Ide

Question

"Good" cholesterol (known as "HDL") is protective against heart disease. Ideally, we hope for levels are those that exceed around 60.

A sample of 200 sedentary males had their HDL levels measured and it was found to be normally distributed N(42, 2.8).

a)      What is the cholesterol level of the highest 20%?

b)      What is the cholesterol range of the people between the 25th and 75th percentiles?

c)      Suppose you decided to bring in all of the people who had levels of 40 or lower in for further dietary counseling. If there were 200 people used in this study, how many people would you anticpate would require counseling?

Please explain your answers.

Thanks!

Explanation / Answer

Part-a

We have to find x0 such that P(X>x0)=0.20 or P(X<x0)=0.80

So, x0== 44.35653945 using excel function =NORMINV(0.80,42,2.8)

Part-b

We have to find x1 such that P(X<x1)=0.25 and x2 such that P(X<x2)=0.75

So, x1= 40.1114287 using excel function =NORMINV(0.25,42,2.8)

And, x2=43.8885713 using excel function =NORMINV(0.75,42,2.8)

Part-c

P(X<40)= 0.237525262 using excel function =NORMDIST(40,42,2.8,TRUE)

So, If there were 200 people used in this study, the number of people would you anticpate would require counseling=200*0.237525262 =47.51=48

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