I. MCAT scores. Suppose that scores on the Medical College Admission Test are distributed approximately normally with u
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I. MCAT scores. Suppose that scores on the Medical College Admission Test are distributed approximately normally with u = 500 and 6 = 10. In each part of this question, use two places after the decimal point for z scores and four places after the decimal point for proportions. For parts 1-4 and 6-9, using and including an appropriate sketch would be wise, but is not required. IN EACH PART, MAKE CLEAR WHAT YOUR ANSWER IS!!! (For all parts that involve distributions of sample means—parts 2-4 and 7-9—you have to calculate and use the standard deviation of a distribution of means for samples of the specified size.) All these questions concern values lower than or parts of distributions below u, so make sure that your answers are consistent with that. (33 pts. — 4 pts per part except 5. which is 1 pt.)
6) How low must an MCAT score be to be in the lowest 2% of the distribution of MCAT scores? 2% 7) How low must the mean of a random sample of 4 MCAT scores be to be in the lowest of the distribution of means of samples of 4? 2% 8) How low must the mean of a random sample of 25 MCAT scores be to be in the lowest of the distribution of means of samples of 25? 2% 9) How low must the mean of a random sample of 100 MCAT scores be to be in the lowest of the distribution of means of samples of 100?