A college admissions officer for an MBA program has determined that historically applicants have undergraduate grade point averages that are normally distributed with standard deviation 0.45. From a random sample of 25 applications from the current year, the sample mean grade point average is 2.90.

a. Find a 95% confidence interval for the population mean. (2 points)

b. Based on these sample results, a statistician computes for the population mean a confidence interval extending from 2.81 to 2.99. Find the confidence level associated with this interval. (2 points)

c. Test at the 10% level the null hypothesis that the population mean grade point average is at least 2.65. (3 points)

d. Calculate Type II Error. (3 points)