Question

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The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with a mean of 150 and a standard deviation of 8.8. In addition to other qualifications, a score of at least 152 is required for admission to a particular graduate school.

a )Determine the 80^thpercentile of GRE scores.

b) Determine the GRE scores that make up the middle 95% of all scores.

c) Compare the results in part b) to the values given by the Empirical Rule.

Answer 1

Let X denotes the score of a randomly selected student on the quantitative portion.

X ~ Normal(150, 8.8²)

a) To find 80^thpercentile of GRE scores, i.e.

b) To find the middle 95% of all scores, i.e. to find x₁ and x₂ such that

So, we can write

and

c) By the Empirical Rule.

95% values will lie between ( mean - 2*standard deviation, mean + 2*standard deviation) = (150 - 2*8.8, 150 + 2*8.8) = (132.4, 167.6)