(a) How many standard deviations above the mean did Sophia score on the Verbal Reasoning section? (b) How many standard deviations above the mean did Sophia score on the Quantitative Reasoning section? (c) What percent of people scored better than Sophia on the Verbal section
Sophia took the Graduate Record Examination (GRE). She scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. Suppose that the mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 9, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 2. Suppose that both distributions are nearly normal.
(a) How many standard deviations above the mean did Sophia score on the Verbal Reasoning section?
(b) How many standard deviations above the mean did Sophia score on the Quantitative Reasoning section?
(c) What percent of people scored better than Sophia on the Verbal section?
(d) What percent of people scored better than Sophia on the Quantitative section?
X1=Verbal Reasoning section
X2=Quantitative Reasoning section
X1~N( μ1=151 , ?1=9 )
μ1 =151 , ?1 = 9 , X1=160
X2~N( μ2=153 , ?2=2 )
μ2 =153 , ?2 = 2 , X2=157
Z-score =( x - μ )/?
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