## (Solution document) (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...

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]

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