Question

2. GMAT scores are required for admission to JHJ’s MBA program. GMAT scores are known to be normally distributed with a mean of 490 points and a standard deviation of 61 points. a. 25% of the scores of applicants are less than what score? b. 75% of the scores of applicants are less than what score? c. 25% of the scores of applicants are less than what score? d. 80% of the scores of applicants are more than what score? e. Only applicants in the top 10% of all GMAT scores, are admitted to the MBA program. What score is required to be admitted to the MBA program.

Answer 1

Solution:

Given: MAT scores are known to be normally distributed with a mean of 490 points and a standard deviation of 61 points.

Thus : and

Part a) 25% of the scores of applicants are less than what score?

That is: find x value such that:

P( X < x ) = 25%

P( X < x ) =0.25

Thus find z value such that:

P( Z< z ) = 0.25

Look in z  table for Area = 0.2500 or its closest area and find corresponding z value.

Area 0.2514 is closest to 0.2500 and it corresponds to -0.6 and 0.07

that is  z = -0.67

Now use following formula to find x value:

Thus 25% of the scores of applicants are less than 449.13.

( Note: Round answer to specified number of decimal places )

Part b) 75% of the scores of applicants are less than what score?

That is: find x value such that:

P( X < x ) = 75%

P( X < x ) =0.75

Thus find z value such that:

P( Z< z ) = 0.75

Look in z  table for Area = 0.7500 or its closest area and find corresponding z value.

Area 0.7486 is closest to 0.7500 and it corresponds to 0.6 and 0.07

that is  z = 0.67

Now use following formula to find x value:

Thus 75% of the scores of applicants are less than 530.87

Part c) 25% of the scores of applicants are less than what score?

( Note: question in part c is same as question in part a, if it is same, then answer is same:

25% of the scores of applicants are less than 449.13.)

Part d) 80% of the scores of applicants are more than what score?

That is: find x value such that:

P( X > x ) = 80%

P( X > x ) =0.80

Thus find z value such that:

P( Z > z ) = 0.80

That is find z such that:

P( Z < z ) = 1 - P( Z > z )

P( Z < z ) = 1 - 0.80

P( Z < z ) = 0.20

Look in z  table for Area = 0.2000 or its closest area and find corresponding z value.

Area 0.2005 is closest to 0.2000 and it corresponds to -0.8 and 0.04

that is  z = -0.84

Now use following formula to find x value:

thus 80% of the scores of applicants are more than 438.76.

Part e)  Only applicants in the top 10% of all GMAT scores, are admitted to the MBA program. What score is required to be admitted to the MBA program?

That is find x value such that;

P( X > x ) = 10%

P( X > x ) =0.10

Thus find z value such that:

P( Z > z ) = 0.10

That is find z such that:

P( Z < z ) = 1 - P( Z > z )

P( Z < z ) = 1 - 0.10

P( Z < z ) = 0.90

Look in z  table for Area = 0.9000 or its closest area and find corresponding z value.

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

that is  z = 1.28

Now use following formula to find x value:

Thus 568.08 score is required to be admitted to the MBA program.

( Note: Round answer to specified number of decimal places )