Question

3) Scores on the verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 119. Scores on the quantitative GRE have a mean of 584 and a standard deviation of 151. Assume the scores are normally distributed.

a) Suppose a graduate program requires students to have verbal and quantitative scores at or above the 90th percentile. What is the verbal score (to the whole point) required? (1 point)

b) What is the quantitative score required at or above the 90th percentile? Round to the whole point. (1 point)

c) A perfect score on either exam is 800. What percentage of students score 800 on the verbal exam? Round to the hundredths of a percent as needed. (1 point)

d) A perfect score on either exam is 800. What percentage of students score 800 on the quantitative exam? Round to the tenths as needed. (1 point)

e) If someone scored higher than 2.5% of the quantitative test takers, what is that score?

Answer 1

Let the subscript 1 denote the Verbal GRE scores and 2 denote the Quantitative GRE. It is given that verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 119. Scores on the quantitative GRE have a mean of 584 and a standard deviation of 151. Assume the scores are normally distributed.

ie

  

From Normal theory we know that and      will have a standard Normal variate.

a) Suppose a graduate program requires students to have verbal and quantitative scores at or above the 90th percentile. What is the verbal score (to the whole point) required? (1 point).  

Now 90 th percentile implies . Because 90th percentile is the cumulative probability measuring 0.9 from .

From tables or from the EXCEL function(NORM.S.INV(0.9) we find that the =1.2816.

ie

Therefore the Verbal score to be at or above the 90th percentile=613.

b) What is the quantitative score required at or above the 90th percentile? Round to the whole point. (1 point)

A before, we shall have to find the

  

  

  

Therefore, the quantitative score required at or above the 90th percentile=778.

c) A perfect score on either exam is 800. What percentage of students score 800 on the verbal exam? Round to the hundredths of a percent as needed.

The required percentage is given by

Therefore will give the percentage of students who scored more than 800.(Since it is a normal distribution the probability at a particular point is zero since it is a continuous distribution).

Therefore,percentage of students score 800 on the verbal exam=0.2%

d) A perfect score on either exam is 800. What percentage of students score 800 on the quantitative exam? Round to the tenths as needed. (1 point).

This will be

therefore will give the percentage of students who scored more than 800.(Since it is a normal distribution the probability at a particular point is zero since it is a continuous distribution).

Therefore,percentage of students score 800 on the quantitative exam=7.6%

e) If someone scored higher than 2.5% of the quantitative test takers, what is that score?

This means    ,

If someone scored higher than 2.5% of the quantitative test takers, that score is 879.96~880.