3.3 CRE scores, Part I. Sophia who took the Graduate Record Examination (GRE) sc

Question

3.3 CRE scores, Part I. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 137 on the Quantitative Reasoning section The mean score for Verbal Resoning section for all test tabers ws 151 with a standard deviation of 7, and the mean score for the Quantitativn Reseoning wM, 153 with 8tsndard deviation of 7.67. Suppose that both distributions are nearly Dormal. (a) Write down the shoct-hand for these two normal distzibutions (b) What is Sophia's 2-score ce the Verbal Reasooing section? On the Quantitative Reasoning section? Draw a standard normal distuibutlon curve and mark these two 2-scores. (e) What do these Z-soores tell you? ()Relstive to others, which section did he do better on? Find her pecentile cs for the two xa. (f) What percent of the test takers did better than her on the Verbal Reasonimg section? On the a) Explaim why simply comparing raw soores from the two sections could lead to an incorrect (h) If the distribations of the scores on these exams are not nearly normal, woald your answers to Quantitative Reasoning sectio? conclusica as to which socticn a student did better on. parts (b) () change? Expluin your rcasoning

Explanation / Answer

1 - verbal reasoning section
2- quantitative reasoning section

z1 = (X1 - 151)/7
z2 = (X2 - 153)/7.67

b)
z1 = (160 - 151)/7 = 1.2857142

z2 = (157 - 153)/7.67 = 0.5215123

c)
z-score tells how many sd it is away from mean
higher the z-score , the better is performance
d)
since z1 > z2
she did better in verbal reasoning section

e) P(Z < 1.2857142)
= 0.900700

90 percentile in verbal
P(Z < 0.521512)
=0.699000
69.9 percentile in quantitative

f) in verbal
100 - 90 = 10 % did better
in quantitative
100-69.9 = 30.1 %

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