se the following to answer questions 19-21 The GMAT scores of all examinees who

Question

se the following to answer questions 19-21 The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with a mean of 420 and a standard deviation of 46. The probability that the score of a randomly selected examinee is between 400 and 480, rounded to four decimal places, is: 19. 20. The probability that the score of a randomly selected examinee is less than 370, rounded to four decimal places, is: 21. The probability that the score of a randomly selected examinee is more than 530, rounded to four decimal places, is:

Explanation / Answer

mean is 420 and s is 46

z is given as (x-mean)/s

a) P(400<x<480)=P((400-420)/46<z<(480-420)/46)=P(-0.43<z<1.3) or P(z<1.3)-(1-P(z<0.43)) from normal table it is 0.9032-(1-0.6664)=0.5696

b) P(x<370)=P(z<(37-420)/46)=P(z<-1.09) or 1-P(z<1.09)=1-0.8621=0.1379

c) P(x>530)=P(z>(530-420)/46)=P(z>2.39)=1-P(z<2.39)=1-0.9916=0.0084

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