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1. The Graduate Record Examination (GRE) is a test required for admission to man

ID: 3173545 • Letter: 1

Question

1. 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. (Source: www.ets.org) In addition to other qualifications, a score of at least 160 is required for admission to a particular graduate school.

a. Shade the region under the normal curve that represents test takers who scored above 160 in the quantitative portion of the GRE:

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

What proportion of combined GRE can be expected to be under 160?

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

What is the probability that a randomly selected student will score over 145 points?

140 150 160 170

Explanation / Answer

Solution:

Q: What proportion of combined scores can be expected to be over 160?
Ans: P(X>160) = 1-P(X<=160) =1-NORMSDIST((160-150)/8.8)
=0.127902204

Q: What proportion of combined GRE can be expected to be under 160?
Ans: P(X<160) =NORMSDIST((160-150)/8.8)
= 0.872097796


Q: What proportion of combined GRE scores can be expected to be between 155 and 160?
Ans: P(155<X<160) = P(X<=160) - P(X<=155) =
=NORMSDIST((160-150)/8.8)-NORMSDIST((155-150)/8.8)
= 0.157053554

Q: What is the probability that a randomly selected student will score over 145 points?
Ans: P(X>145) = 1 - P(X<145) =1-NORMDIST(145,150,8.8,TRUE)
= 0.715044242