Question 3 . (9 marks ) The following is a sample of scores ( X ) for 36 students in a marketing course SA , 77 84 62 77 86 69 78 86 69 81 87 72 , 82 , 89 72 , 82 90 76 82 , 90 74 , 82 , 92 75 82 92 76 82 92 76 82 94 76 , 84 96 Given the EX = 2900 E ( X - X) = = 2852 889 a ) Find the 90 percent confidence interval for the population mean to b ) Suppose that the average score for all students taking the course is 75 and the standard deviation is 16 what is the probability of getting a sample with a mean as large of greater than 80.56 What is the probability of getting two independent samples each with sample means greater than or equal to 80.56