Question

The serum cholesterol level of U.S. females 20 years old or older is normally distributed with a mean of 220mg.dL (milligrams per deciliter) and a standard deviation of 44 mg/dL. Let X represent serum total cholesterol level for U.S. females 20 years old or older. One outcome of interest is the probability that a woman has a serum cholesterol level greater than 266mg/dL. If 550 U.S. women 20 yrs old or older are randomly selected, how many of them would we expect to have a serum cholesterol level greater than 266 mg/dL? Choose the closest value.

Choices: 37, 514, 0.9332, 0.0668

Answer 1

Probability that a woman has a serum cholesterol level greater than 266mg/dL = P(X > 266)

= P[Z > (266 - 220)/44]

= P[Z > 1.045455]

= 0.1479 (Using Z table)

Number of people have a serum cholesterol level greater than 266 mg/dL = 550 * 0.1479 = 81.345 81

All given choices are incorrect. If the mean is 200 mg/dL then

Probability that a woman has a serum cholesterol level greater than 266mg/dL = P(X > 266)

= P[Z > (266 - 200)/44]

= P[Z > 1.5]

= 0.0668 (Using Z table)

Number of people have a serum cholesterol level greater than 266 mg/dL = 550 * 0.0668 = 36.74 37