Use the following information for problems 1 and 2. Suppose that a committee is studying the amount of time spent commuting to work. Assume the distribution of commute times is normal. The committee randomly surveyed 93 commuters and found the sample mean was 33.3 minutes and the population standard deviation is known to be 10.2 minutes.

1) (8 points) Construct a 90% confidence interval for the population mean commute time.

2) (2 points) Explain in a complete sentence what the confidence interval means.

A sample of 29 small bags of the same brand of candies was selected Assume the distribution of bag weights is normal. The weight of each bag was recorded and the mean was found to be 2 ounces with a sample standard deviation of 0.12 ounces.

3) (8 points) Construct a 90% confidence interval for the population mean weight of bags of candy.

4) (2 points) Explain in a complete sentence what the confidence interval means.

5) (8 points) As of April 7, 2021, 16.9% of the 331,000,000 Americans have received the coronavirus vaccine.

Construct a 99% confidence interval for the population proportion of Americans who have received the coronavirus vaccine.

BONUS (4 POINTS) A company that developed a popular gaming app wants to determine the current percentage of customers who spend more than $5 on in-app purchases. How many customers should the company survey in order to be 95% confident that the estimated proportion is within 2 percentage points of the true population of customers who spend more than $5 on in-app purchases?