To estimate the mean of the DS1000 midterm scores, you obtain a simple random sample (SRS)...

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To estimate the mean of the DS1000 midterm scores, you obtain a simple random sample (SRS) of scores from n = 40 students. From previously published information, you know that the midterm scores are approximately Normal, with a mean of 70 and a standard deviation of 10. a) [3 points] What is the approximate distribution of the sample mean test score X, according to the central limit theorem? b) [2 points] What is the approximate probability that X is above 73? Use Table A. c) [2 points] What is the sample size you need to make the standard deviation of X equal to 1? Why? d) [3 points] Suppose it turns out your SRS gives an observation x = 65. Do you have enough statistical evidence to reject the hypothesis that the true population mean is 70? To estimate the mean of the DS1000 midterm scores, you obtain a simple random sample (SRS) of scores from n = 40 students. From previously published information, you know that the midterm scores are approximately Normal, with a mean of 70 and a standard deviation of 10. a) [3 points] What is the approximate distribution of the sample mean test score X, according to the central limit theorem? b) [2 points] What is the approximate probability that X is above 73? Use Table A. c) [2 points] What is the sample size you need to make the standard deviation of X equal to 1? Why? d) [3 points] Suppose it turns out your SRS gives an observation x = 65. Do you have enough statistical evidence to reject the hypothesis that the true population mean is 70?