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Problem #3: Previous studies show that the average score on the second midterm for an introductory statistics class is 90.36 points with a population standard deviation of 14.30 pomts. Assume the distribution of scores is normal. a. What is the probability that a student scored at least 85 points on the second midterm? b. If a score is considered an A if it falls on the top 10% of the exam scores, what is the minimum score required to get an A? For the next four questions, suppose a random sample of 15 students taking an introductory statistics course is selected. c. What is the probability that the average exam score of these students exceeds 92 points? d. If the sample average exam score was determined to be 87 points, construct and interpret 90% condence interval for the true average exam score. e. Based on the interval in part d, do the data provide evidence to support the claim that the average exam score for the second midterm is 90.36 points? ' f. If the studv is to be repeated and the researchers want to be 95% condent about the .,.- p 7 , eshmate With a maximum error of 3 points, how many students need to be selected