Question

Hi I'm having a hard time understand this can someone please explain it to me? Thank you.

Cholesterol is a type of fat found in the blood. It is measured as a concentration: the number of milligrams of cholesterol
found per deciliter of blood (mg/dL). A high level of total cholesterol in the bloodstream increases risk for heart disease.
For this problem, assume cholesterol in men and women follows a normal distribution, and that “adult man” and “adult
woman” refers to a man/woman in the U.S. over age 20. For adult men, total cholesterol has a mean of 188 mg/dL and a
standard deviation of 43 mg/dL. For adult women, total cholesterol has a mean of 193 mg/dL and a standard deviation
of 42 mg/dL. The CDC defines “high cholesterol” as having total cholesterol of 240 mg/dL or higher, “borderline high” as
having a total cholesterol of more than 200 but less than 240, and “healthy” as having total cholesterol of 200 or less. A
study published in 2017 indicated that about 11.3% of adult men and 13.2% of adult women have high cholesterol.

1) The CDC guidelines for cholesterol health are applied to both men and women, but men and women have different
distributions of total cholesterol.
a. What approximate percent of women have a total cholesterol that would be considered “healthy?” (For this
problem, give your answer as a percent, not a decimal. Round your answer to one decimal place.)
b. What approximate percent of men have a total cholesterol that would be considered “healthy?” (For this
problem, give your answer as a percent, not a decimal. Round your answer to one decimal place.)

2) A group of 256 randomly chosen adult men is selected. How many of them do you expect to have a total cholesterol of less than 200 mg/dL? (Round your answer to one decimal place.)

3) Oatmeal is a food that is high in fiber and low in fat. A dietician says, “People who regularly eat oatmeal tend to have
lower cholesterol.” A group of 121 randomly selected adult women who regularly eat oatmeal has a sample mean
total cholesterol of 185 mg/dL.
a. What is the probability a randomly selected group of adult women has a sample mean total cholesterol of 185
or less?
b. Would this be a significant result? (Choose one.)
A. Yes B. No C. Not enough information

Answer 1

1)

a)

µ =    193          
σ =    42
P( X ≤    200   ) = P( (X-µ)/σ ≤ (200-193) /42)      
=P(Z ≤   0.17   ) =   0.5662 or 56.6% (answer)

b)

µ =    188          
σ =    43          
              
P( X ≤    200   ) = P( (X-µ)/σ ≤ (200-188) /43)      
=P(Z ≤   0.28   ) =   0.6099 or 61.0% (answer)

=============

2) expected number = 61.0% * 256 = 156.1 people

3)

a)

µ =    193                                      
σ =    42                                      
n=   121                                      
                                          
X =   185                                      
                                          
Z =   (X - µ )/(σ/√n) = (   185   -   193.00   ) / (   42.000   / √   121   ) =   -2.095  
                                          
P(X ≤   185   ) = P(Z ≤   -2.095   ) =   0.0181                       (answer)

b) NO, because probability is less than 0.05