The Graduate Management Aptitude Test GMAT produced by the E

The Graduate Management Aptitude Test (GMAT), produced by the Educational Testing Service (ETS) in Princeton, New Jersey, is widely used by graduate schools of business in the U.S. as an entrance requirement. Assume that the scores in a recent year are normally distributed with a mean of 494 and a variance of 10,000.

1. What is the probability that a randomly selected score from this administration of the GMAT is between 505 and 687? (You might recall that the orbital period of Mars is about ____ days)

2. What is the probability that a randomly selected score is greater than 384?

Solution

Probability that Score less than 605 is calculated as below

z=(x-mu)/standard deviation

z=505_494/100=0.16

Prob(X<505) would be the value shown in z table for calculated z value above we get Prob(X<505)=0.43644

Similarly we can calculate prob for x<687

Pr(x<687) is (687-494)/100=1.93 then z=0.9732

Hence we need Pr(x<687)-Pr(x-494)=0.9732-0.5636=0.4096

Ans 2

Prob(x<384) when z=(384-494)/100=1

Prob(x<384)=0.8414