1. A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 4 hours and a standard deviation of 2.5 hours. Show all work. Just the answer, without supporting work, will receive no credit. 

(a)  What is the probability that a randomly selected adult has at least 5 hours of exercise per week (round the answer to 4 decimal places)       

(b) Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)

2. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 10. Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment. Show all work.

3. Mimi conducted a survey on a random sample of 100 adults. 75 adults in the sample chose banana as his / her favorite fruit. Construct a 90% confidence interval estimate of the proportion of adults whose favorite fruit is banana. Show all work.   

4. A researcher is interested in testing the claim that more than 80% of the adults believe in global warming. She conducted a survey on a random sample of 800 adults. The survey showed that 650 adults in the sample believe in global warming.  

Assume the researcher wants to use a 0.05 significance level to test the claim. Show all work.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.  

(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.  

(d) Is there sufficient evidence to support the claim that more than 80% of adults believe in global warming? Explain. 

5. Mimi joined a basketball team in spring 2016. On average, she is able to score 20% of the field goals. Assume she tries 10 field goals in a game.    

(a) Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that Mimi scores at least 3 of the 10 field goals. (round the answer to 3 decimal places) Show all work.