The Graduate Record Examinations (GRE) are widely used to help predict the perfo

Question

The Graduate Record Examinations (GRE) are widely used to help predict the performance of applicants to graduate schools. The Faculty of Graduate Studies at a university finds that the scores of its applicants a on the quantitative GRE are normally distributed with a mean of $44 and standard deviation of 103. a) Find the probability that the quantitative GRE of a randomly selected applicant is over 700. b) If they will only consider the top 15% of all applicants for admission, what is the minimum quantitative GRE necessary to be considered for admission? c) Find the probability that the mean quantitative GRE of a random sample of 10 applicants is between 475 and 554.

Explanation / Answer

3.

Mean = 544

Stdev = 103

a. P(X>700) = P(Z> 700-544/103) = P(Z>1.514) = .9354

b. P(X>=c) = .15, (c-544)/103 = 1.035, c = 544+103*1.035 = 650.605

c. P(475<X<554) = P( (475-544)/(103/sqrt(10))<Z<(554-544)/(103/sqrt(10)) = P(-2.1<Z<0.31)

= 0.6217-.0179

= 0.6038

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