Question

1. 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.

1. 25% of the scores of applicants are less than what score?
2. 75% of the scores of applicants are less than what score?
3. 25% of the scores of applicants are less than what score?
4. 80% of the scores of applicants are more than what score?
5. 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

1. Let "X" be the GMAT score.

Therefore,

a) The score such that 25% of the scores of applicants are less than that is obtained by:

### Where P^-1 is inverse cdf of standard normal distribution.

### By using z table

Thus 25% of scores are less than 449

a) The score such that 75% of the scores of applicants are less than that is obtained by:

### Where P^-1 is inverse cdf of standard normal distribution.

### By using z table

Thus 75% of scores are less than 531

c) The question is same as a) Therefore, 25% of scores are less than 449.13

d)

The score such that 80% of the scores of applicants are less than that is obtained by:

### Where P^-1 is inverse cdf of standard normal distribution.

### By using z table

Thus 80% of scores are less than 541

e) Given Only applicants in the top 10% of all GMAT scores, Therefore the score such that top 10% of students score that that is given by:

### Where P^-1 is inverse cdf of standard normal distribution.

### By using z table

Therefore the score required to be admitted to the MBA program is 468.