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. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places)
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 490 and 520? (Round your answer to four decimal places)