Question

Hi can someone please actually EXPLAIN how to do this? I'm really confused on how to get the answers

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) 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?

2) 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.)

The manufacturer of a certain electronic component claims that they are designed to last just slightly more than 4 years because they believe that customers typically replace their device before then. Based on information provided by the company, the components should last a mean of 4.24 years with a standard deviation of 0.45 years. For this scenario, assume the lifespans of this component follow a normal distribution

3) The company considers a component to be “successful” if it lasts longer than the warranty period before failing. They estimate that about 70.3% of components last more than 4 years. They find a random group of 10 components that were sold and count the number of them which were “successful,” lasting more than 4 years.

a. What is the expected number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.)

b. What is the standard deviation for the number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.)

c. What is the probability that at least 8 of these components will last more than 4 years?

4) The company is not satisfied with how many returns they are processing, and accountants in the company are recommending that they change the warranty period. The accountants suggest basing the period of the warranty on making sure, in the long run, only about 5% of customers will return the component. What amount of time corresponds to the shortest 5% of lifespans for this component? (Round your answer to 1 decimal place.)

Answer 1