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Low values HDL (High density lipoprotein) have been found to be associated with

ID: 3074782 • Letter: L

Question

Low values HDL (High density lipoprotein) have been found to be associated with increased risk of heart disease. Assume that HDL levels in a population of women (ages 20 years or more) are approximately normally distributed with mean mu= 55 mg/dL and standard deviation sigma=15.5 mg/dL.

a) Find the probability that a woman in this population chosen at random will have HDL less than 40 mg/dL? (This is below the recommended level of HDL)

b) Find the percent of women who are considered to have a protective level of HDL which is 60 mg/dL or greater.

c) Compute the proportion of women who have HDL levels between 40 and 60 mg/dL.

d) A patient’s HDL level is higher than 75% of the values in this population. Find that patient’s HDL level.

e) A patient’s HDL level is in the lowest 10th percentile. Find that patient’s HDL level.  

Explanation / Answer

a)

mu= 55

sigma= 15.5

X= 40

Z=(X-mu)/sigma

=-0.96774

probability =P(Z<-0.96774)

=0.16658

b)

mu= 55

sigma= 15.5

X= 60

Z=(X-mu)/sigma

=0.322580

probability =P(Z>0.32258)

=0.373506

in percentage = 37.35%

c)

mu= 55

sigma= 15.5

X= 60

Z=(X-mu)/sigma

0.322580

probability P1=P(Z<0.32258)

p1= 0.626493

mu= 55

sigma= 15.5

X= 40

Z=(X-mu)/sigma

-0.96774

probability P2=p(Z<-0.966774)

p2= 0.166586634

Required probability is (P1-P2)=0.459906

proportion is 0.4599

d)

mu= 55

sigma= 15.5

X= unknown

probability= 0.75

z-score for probability=0.67448

Z=(X-mu)/sigma

x=(mu+Z*sigma)

x= 65.45459

HDL level =65.45 mg/dL

e)

mu= 55

sigma= 15.5

X= unknown

probability= 0.1

z-score for probability=-1.281551

Z=(X-mu)/sigma

x=(mu+Z*sigma)

x= 35.1359

HDL level= 35.1359 mg/dL

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