Question

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation of 8.8. In addition to other qualifications, a score of at least 160 is required for admission to a particular graduate school.

a. What proportion of combined scores can be expected to be over 160?

b. What proportion of combined GRE scores can be expected to be between 155 and 160?

c. What is the probability that a randomly selected student will score less than 150 points?

d. Historically, Department of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. What is the lowest GRE score of the students they admit?

e. Determine the range of scores that make up the middle 95% of the scores.

Answer 1

a) Proportion of combined scores can be expected to be over 160, P(X>160) =

b) Proportion of combined GRE scores can be expected to be between 155 and 160, P(155< X<160) =

c) Probability that a randomly selected student will score less than 150 points, P(X<150) =

d) From the standard normal table the value of Z that is atleast 0.61 (or less than 0.39) is -0.279.

Lowest GRE score of the students they admit, X =

e) middle 95% mean 2.5% area is on both sides.

From the standard normal table the z value at 0.025 are 1.96

Lower score, X

Lower score, X

the range of score is 167.248- 132.752 = 34.496