Reference no: EM132907532

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. Oatmeal is a food that is high in fiber and low in fat. A dietician says, "People who regularly eat oatmeal tend to have lower cholesterol." A group of 121 randomly selected adult women who regularly eat oatmeal has a sample mean total cholesterol of 185 mg/dL.

a. What is the probability a randomly selected group of adult women has a sample mean total cholesterol of 185 or less? (4 pt)

b. Would this be a significant result? (Choose one.)

A. Yes B. No C. Not enough information

2. 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?

3. 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.)