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 D to the values given by the Empirical Rule.

Answer 1

Mean=150, Sd=8.8

A) 80th percentile,

P(X<x)=.80

P(X-mean/sd<x-mean/sd)=.80

P(z<x-mean/sd)=.80

And from z table p(z<0.84)=.80

On camparing (x-mean/sd)=.84

x=mean+0.84*sd=150+0.84×0.84=157.39

GRE score for 80th perxentile=157.39

B) 95% area is coverd by

Lower bound (mean-1.96*sd) =150-1.96*8.8=132.75

Upper bound (mean+1.96*sd)= 150+1.96*8.8=167.25

C)under emprical rule

95% area is coverd by

Lower bound (mean-2sd)=150-2*8.8= 132.4

Upper bound (mean+2sd)=150+2*8.8=167.6