The total cholesterol levels of a sample of men aged 35-44 are normally distribu

Question

The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 225 mg/dL and a standard deviation of 36.7 mg/dL. What percent of the men have a total cholesterol level less than 233 mg/dL of blood? If 253 men in the 35-44 age Group are randomly selected, about how many would you expect to have a total cholesterol level greater than 255 mg/dL of blood? The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 225 mg/dL and a standard deviation of 36.7 mg/dL. What percent of the men have a total cholesterol level less than 233 mg/dL of blood? If 253 men in the 35-44 age Group are randomly selected, about how many would you expect to have a total cholesterol level greater than 255 mg/dL of blood?

Explanation / Answer

from normal distribution z=(X-mean)/std deviation

hence P(X<233)= P(Z<(233-225)/36.7)=P(Z<0.218)=0.5863

for 253 men;

hence P(X>255)=1-P(X<255)=1-P(X<(255-225)/36.7)=1-P(Z<0.8174)=1-0.7932=0.2068

hence expected number of people =np=253*0.2068~52

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