Answer to Question #336695 in Statistics and Probability for felicity

Question

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)

Answer 1

a.

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

b.

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

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

c.

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

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