Based on the performance of all individuals who tested between July 1, 2013 and

Question

Based on the performance of all individuals who tested between July 1, 2013 and June 30, 2016, the GRE Quantitative Reasoning scores are normally distributed with a mean of 152.57 and a standard deviation of 9.02. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work. Just the answer, without supporting work, will receive no credit.

(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places)

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is greater than 155? (Round your answer to four decimal places)

Explanation / Answer

Part-a

the standard deviation of the sample means=sigma/sqrt(n)=9.02/sqrt(64) =1.1275

Part-b

Z-score for mean = (155-152.57)/1.1275 =2.1552

So P(mean>155)=P(Z>2.1552) =1-P(Z<2.1552) =1-0.9844=0.0156

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