9. 0/3 points | Previous Answers MBasicStat7 15.E.028. My Notes Ask Your Teacher

Question

9. 0/3 points | Previous Answers MBasicStat7 15.E.028. My Notes Ask Your Teacher Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 5.3. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 25.0 the MCAT on your campus is 325 oshed information you know ha (a) If you choose one student at random, what is the probability that the student's score is between 20 and 30? (Round your answer to four decimal places.) (b) You sample 25 students. What is the standard deviation of sampling distribution of their average score X? (Enter your answer to two decimal places.) (c) What is the probability that the mean score of your sample is between 20 and 30? (Round your answer to four decimal places.) You may need to use the appropriate Appendix Table to answer this question

Explanation / Answer

solution:-
a. z-score for 30 = (30 - 25) / 5.3 = 0.9434
z-score for 20 = (20 - 25) / 5.3 = -0.9434
Probability ( 20 < X < 30 ) = 0.8264 - 0.1736 = 0.6528
b) standard deviation of the sample = 5.3 / square root(25) = 1.06

c) z-score for 30 = (30 - 25) / 1.06 = 4.7169
z-score for 20 = (20 - 25) / 1.06 = -4.7169

Probability ( 20 < X < 30 ) = 1-0 = 1

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