A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 458.

Assume the population standard deviation is σ = 116.

a. Construct a 99% confidence interval for the mean mathematics SAT score for the entering freshman class.

b. If the sample size were 75 rather than 100, would the margin of error be larger or smaller than the result in part (a)?

Explain.

c. If the confidence level were 95% rather than 99%, would the margin of error be larger or smaller than the result in part (a)? Explain.

d. Based on the confidence interval constructed in part (a), is it likely that the mean mathematics SAT score for the entering freshman class is greater than 500?