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 207 milligrams per deciliter and a standard deviation of 37.4 milligrams per deciliter. (a) What percent of the men have a total cholesterol level less than 23.1 milligrams per deciliter of blood? (b) If 248 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol of level greater than 252 milligrams per deciliter of blood? (a) The percent of the men a total cholesterol level less than 231 milligrams per deciliter of blood is %. (b) Of the 248 men selected. would be expected to have a total cholesterol level greater than 252 milligrams per deciliter of blood is % (b) Of the 248 men selected. would be expected to have a total cholesterol greater than 252 milligrams per deciliter of blood.

Explanation / Answer

Given , params of normal distribution:

Mean = 207
Stdev = 37.4

a. P(X<231) = P(Z< (231-207)/37.4)=P(Z<.641) =0.7389

b. P(X>252) = P(Z> (252-207)/(37.4) = P(Z>1.2) =1-.8849 = .1151

So, .1151*248 = 28.5 or 29 people out of 248 people have score above 252

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