1. (35 points) Suppose serum folic acid levels in child-bearing women in U.S. population is Normally distributed with a population mean of 35.8 nmol/L and a population standard deviation of 13.9 nmol/L.

Find the 95^thpercentile of serum folic acid levels in child-bearing women in U.S. population?

What proportion of the U.S. population has folic acid levels below 18 nmol/L?

Suppose you take a random sample of10child-bearing women from U.S population what is the probabilitynone of them have folic acid less than 18 nmol/L. (Hint:Use your answer to part b to solve this question)

Suppose you plan to take a random sample of15child-bearing women from U.S population and calculate the sample mean. What is the probability the sample mean will begreater than 40 nmol/L?

2. (25 points) Suppose that an influenza epidemic strikes a city. In10%of the families the mother has influenza; in10%of the families the father has influenza and in2%of the families both the mother and father have influenza.

a. Is the event of the mother has influenzamutually exclusivefrom the event the father has influenza?Why briefly.

b. Is the event of the mother having influenzaindependentfrom the event the father has influenza?Why briefly.

c. What is the probabilityeitherthe motherorthe father has influenza?

3. (5 points) Based on the central limit theorem, which distribution is likely to be the sampling distribution of the sample mean with thesmallest standard error, RED or BLACK? Explain briefly.

4. (25 points; 5 points each)

The results of a study in 2022 of a random sample of 30 federal employees reported the following summary statistics:

Sample mean age was 36.5

Sample standard deviation 9.1

Sample proportion of persons without a college degree was 58%.

Answer the following questions

Calculate a95%Confidence interval for the population mean age of federal employees.

In 1990, the average age of the federal employee was 32. Based on your answer topart a,is there any evidence to suggest the population mean average age of a federal employee is older than in 1990?Why?

Calculate a99%Confidence interval for the population proportion of federal employees that do not have a college degree?

If we calculated a99% confidence interval in part a, instead of a 95% confidence interval, the margin of error would _______________: (choose one )

increase

decrease

stay the same

If we increase the sample size to 90 persons, but the reported sample mean and sample standard deviation stayed the same as in part a, the 95% confidence interval for population mean would get___________________: (choose one )

wider

narrower

stay the same

5. (10 points) A poll reported that 64% of the persons sampled agree that American democracy is in crisis and at risk of failing. Suppose you want to repeat this poll, but you want to ensure the margin of error is no more than 2%. How large of a sample size do you need?

10