3. (10 points) The SAT scores are normally distributed.
3. (10 points) The SAT scores are normally distributed. A simple
random sample of 225 SAT scores has a sample mean of 1500 and a sample standard deviation of 300.
(a) (2 pt) What distribution will you use to determine the critical value? Why?
(b) (6 pts) Construct a 95% confidence interval estimate of the mean SAT score. (Show work and round the answer to two decimal places)
(c) (2 pt) Is a 99% confidence interval estimate of the mean SAT score wider than the 95% confidence interval estimate you got from part (b)? Why? [You don’t have to construct the 99% confidence interval]