Answer to Question #336695 in Statistics and Probability for felicity

Question #336695

Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 506 and a standard deviation of 96. (14 pts)


a. What is the probability of an individual scoring above 520? (with illustration, 6 pts)


b. What is the probability of an individual scoring below 506? (with illustration, 4 pts)


c. What is the probability of an individual scoring from 387 to 712? (with illustration, 4 pts)


1
Expert's answer
2022-05-04T12:59:52-0400

a.


P(X>520)=1P(Z52050696)0.4420P(X>520)=1-P(Z\le\dfrac{520-506}{96})\approx0.4420

b.


P(X<506)=P(Z<50650696)P(X<506)=P(Z<\dfrac{506-506}{96})




=P(Z<0)=0.5=P(Z<0)=0.5

c.


P(387<X<712)=P(Z<71250696)P(387<X<712)=P(Z<\dfrac{712-506}{96})




P(Z38750696)0.8765-P(Z\le\dfrac{387-506}{96})\approx0.8765


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