Question 1 (14 marks! A college admissions officer for an MBA program has determined that historically applicants have undergraduate grade points that are normally distributed with standard deviation 0.44. A random sample of applicants is drawn from the current year. (a) Based on these sample results, a statistician computes for the population mean grade points a 95% confidence interval extending from 3.4768 to 37232. Find the sample mean, sampling error and the sample size associated with this interval. (7 marks) (b) With the same level of confidence in part (a), if the standard deviation changes to 0.6, to keep the width of the confidence interval unchanged, how many additional applicants should be added to the sample? {4 marks) (c) The grade points of applicants are unlikely to be normally distributed. Does this invalidate the confidence interval developed in part (a)? Explain