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 204 milligrams per deciliter and a standard deviation of 37.3 milligrams per deciliter. (a) What percent of the men have a total cholesterol level less than 216 milligrams per deciliter of blood? (b) If 244 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 259 milligrams per deciliter of blood? (a) The percent of the men that have a total cholesterol level less than 216 milligrams per deciliter of blood is %. (Round to two decimal places as needed.) (b) Of the 244 men selected, would be expected to have a total cholesterol level greater than 259 milligrams per deciliter of blood. (Round to the nearest integer as needed.)

Explanation / Answer

(a)

Mean of cholestrol level = 204
Standard deviation of cholestrol level, Sd = 37.3

Percent of men having cholestrol level less than 216 mg per decilitre =
P(X < 216) = P(Z < (216 - 204)/37.3) = P(Z < 0.3217)

Using z distribution table, P(Z < 0.3217) = 0.62616
So, Percent of men having cholestrol level less than 216 mg per decilitre = 62.62%

(b)

Probability of men having cholestrol level less than 259 mg per decilitre =
P(X > 259) = P(Z > (259 - 204)/37.3) = P(Z > 1.4745)

Using z distribution table, P(Z > 1.4745) = 0.0702

So, Number of people expected to have total cholestrol level greater than 259 mg per decilitre = 244 * 0.0702 = 17.1288

So, 17 people expected to have total cholestrol level greater than 259 mg per decilitre.

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