The Graduate Record Examination (GRE) test administered by the Educational Testi

Question

The Graduate Record Examination (GRE) test administered by the Educational Testing Service (ETS) has mean scores mu = 500 and standard deviation sigma = 100. The distribution of scores is roughly normal. What is the approximate probability that a single prospective graduate student randomly chosen from all those taking the test will score 550 or higher? Now take a random sample of 30 students who took the test. What are the mean and standard deviation of the sample mean GRE score X- of these 30 students? What is the approximate probability that the mean GRE score X- of these students is 550 or higher? Is the result in (a) more accurate or the one in (c) is? Justify your answer.

Explanation / Answer

a. P[X>550] = P[Z>0.5] = 1 - 0.6915 = 0.3085

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