To estimate the mean of the DS1000 midterm scores, you obtain a simple random sample (SRS) of scores from n = 50 students. From previously published information, you know that the midterm scores are approximately Normal, with a mean of 75 and a standard deviation of 10. a) [3 points] What is the approximate distribution of the sample mean test score, , according to the central limit theorem? b) [2 points] What is the approximate probability that is above 78? Use Table A. c) [2 points] What is the sample size you need to make the standard deviation of the sample mean equal to 1? Why? d) [3 points] Suppose it turns out your SRS gives an of 74. Do you have enough statistical evidence to reject the hypothesis that the true population mean is 75