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19 Sampling Distribution for a Mean: Problem 9
(1 point)
Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean
score $\mu$ of those who took the MCAT at Etown, you obtain a simple random sample of 28 students' scores. The scores follow a normal
distribution, and from published information you know that the standard deviation is 6.4. Suppose that (unknown to you) the mean score of
those taking the MCAT at Etown is 25.
(a) If you choose one MCAT score at random, then what is the probability that the student's score is between 20 and 30?
(b) What is the probability that the mean score of your sample is between 20 and 30?
Note: You can earn partial credit on this problem.
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