SAT math scores are normally distributed with a standard deviation of 100. A simple random sample of 30 seniors had a sample mean of 635 a- Find the 99% confidence interval for the mean b- If the...

SAT math scores are normally distributed with a standard deviation of 100. A simple random sample of 30 seniors had a sample mean of 635

a- Find the 99% confidence interval for the mean

b- If the national average is 550, is this sample evidence that this group of seniors is really exceptional? Write appropriate null and alternate hypotheses, find the p-value and interpret your results.