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 8.8. In addition to other qualifications, a score of at least 165 is required for admission to a particular graduate school.

A) Describe how you would shade the region under the normal curve that represents test takers who scored above 165 in the quantitative portion of the GRE.

B) What proportion of GRE scores can be expected to be over 165? (rounded to hundredths)

C) What proportion of GRE scores can be expected to be under 165?

D) What proportion of GRE scores can be expected to be between 155 and 165?

E) What is the probability that a randomly selected student will score less than 145 points?

F) Determine the 75th percentile of the GRE scores (rounded to a whole number)

G) Determine the range of scores that make up the middle 90% of all scores (rounded to whole numbers). Low bound and high bound?

Suppose n = 16 randomly selected students take the GRE on the same day.

Describe the sampling distribution of the sample mean for the quantitative GRE Scores for the 16 students.

H) The Shape is

I) The Mean is

J) The Sd is

K) What is the probability that a random sample of 16 students has a mean score on the GRE that is less than 147?

L) Would this (K) be an unusual outcome?

M) What is the probability that a random sample of 16 students has a mean score on the GRE that is greater than 165?

Answer 1

Solution:-) We have the following information,

Score of atleast 165 is required for admission to a particular graduate school.

A) The graph is represented as

Now, for other problems, R code will be used. On R.H.S. is R-output and on L.H.S. is R-Code

the sampling distribution of the sample mean for the quantitative GRE Scores for the 16 students.

H) The Shape is Normal

I) The Mean is 150.

J) The Sd is