Question

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) A researcher measures the total cholesterol of a randomly selected group of 36 adult women, and counts the number of them who have high cholesterol. (Assume that 13.2% of adult women have high cholesterol.)

a. What is the probability that exactly 4 of these 36 women have high cholesterol?

b. What is the probability that 8 or less of these 36 women have high cholesterol?

2) A doctor recommends drastic lifestyle changes for all adults who are in the top 5% of total cholesterol levels.

a. What total cholesterol level is the cutoff for the top 5% of women? (Round to 1 decimal place.)

b. What total cholesterol level is the cutoff for the top 5% of men? (Round to 1 decimal place.)

Answer 1

1)

n= 36

probability of having high cholesterol = 13.2% = 0.132

P ( X =    4   ) = C(36,4) * 0.132^4 * (1-0.132)^32 =            0.1928

.....

X	P(X)
0	0.0061
1	0.0335
2	0.0892
3	0.1537
4	0.1928
5	0.1876
6	0.1474
7	0.0961
8	0.0530

p(x=<8) = sum of probability from x=0 to x=8

= 0.9593

..........

2)

µ=   193                  
σ =    42                  
proportion=   0.95                  
                      
Z value at    0.95   =   1.64   (excel formula =NORMSINV(   0.95   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.64   *   42   +   193  
X   =   262.1 (answer)          

..........

B)

µ=   188                  
σ =    43                  
proportion=   0.95                  
                      
Z value at    0.95   =   1.64   (excel formula =NORMSINV(   0.95   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.64   *   43   +   188  
X   =   258.7   (answer)          

PLEASE revert back for doubt

thanks