Question

Amanda took the Graduate Record Examination (GRE), and scored 160 in verbal reasoning and 157 in quantitative reasoning. The mean score for verbal reasoning was 151 with a standard deviation of 7, compared with mean µ = 153 and σ = 7.67 for quantitative reasoning. Assume that both distributions are normal.

(a) What were Amanda’s Z-scores on these exam sections? Mark these scores on a standard normal distribution curve.

(b) Which section did she do better on, relative to other students?

(c) Find her percentile scores for the two exams.

Answer 1

a)

for verbal-

µ=   151
σ=   7.0000
X=   160

Z=(X-µ)/σ=   (160-151)/7=       1.29
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for quantitaive-

µ=   153
σ=   7.6700
X=   157

Z=(X-µ)/σ=   (157-153)/7.67=       0.52

b)

she scored better in verbal reasoning

c)

P( X ≤    160   ) = P( (X-µ)/σ ≤ (160-151) /7)      
=P(Z ≤   1.29   ) =   0.9007   (answer)
percentile score in verbal = 90.07

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P( X ≤    157   ) = P( (X-µ)/σ ≤ (157-153) /7.67)      
=P(Z ≤   0.52   ) =   0.6990

percentile score in quantitaive = 69.90 (answer)