1. A research concludes that the number of hours of exercise per week for adults is normally distributed w ith 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 75 th percentile for the distribution of exercise time per wee k . ( 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 cred it.
(a) Consider all random samples of 6 4 test score s. What is the standard deviation of the sample means ? (Round your answer to three decimal places)
(b) What is the probability that 6 4 randomly selected test scores will have a mean test score that is between 4 90 and 5 20 ? (Round your answer to four decimal places)