Question

Sophia took the Graduate Record Examination (GRE) and scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for the Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning section was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal. a) Write down the shorthand for these two normal distributions. Verbal Reasoning: N(μ = 151, σ = 7) Quantitative Reasoning: N(μ = 153, σ = 7.67) b) What are Sophia's z-scores on both the Verbal Reasoning section and the Quantitative Reasoning section? What do these z-scores tell you? Round your z-scores to 2 decimal places. She scored 0.86 standard deviations above the mean on the Verbal Reasoning section and 0.26 standard deviations above the mean on the Quantitative Reasoning section. c) Relative to others, which section did she do better on? d) Find her percentile scores for the two exams. Round to the nearest whole percent. Verbal Reasoning: Quantitative Reasoning: e) What percent of the test takers did better than her on the Verbal Reasoning section? Round to the nearest whole percent. What percent of the test takers did better than her on the Quantitative Reasoning section? Round to the nearest whole percent. f) Explain why simply comparing raw scores from the two sections could lead to an incorrect conclusion as to which section a student did better on. We cannot compare the raw scores because they are different tests. We cannot compare the raw scores because we do not have enough information about the other test-takers. We cannot compare the raw scores because they come from different distributions. We can compare the raw scores.

Sophia took the Graduate Record Examination (GRE) and scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for the Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning section was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.

a) Write down the shorthand for these two normal distributions.
Verbal Reasoning: N(μ = 151, σ = 7)
Quantitative Reasoning: N(μ = 153, σ = 7.67)

b) What are Sophia's z-scores on both the Verbal Reasoning section and the Quantitative Reasoning section? What do these z-scores tell you? Round your z-scores to 2 decimal places.
She scored 0.86 standard deviations above the mean on the Verbal Reasoning section and 0.26 standard deviations above the mean on the Quantitative Reasoning section.

c) Relative to others, which section did she do better on?

d) Find her percentile scores for the two exams. Round to the nearest whole percent.
Verbal Reasoning:
Quantitative Reasoning:

e) What percent of the test takers did better than her on the Verbal Reasoning section? Round to the nearest whole percent. What percent of the test takers did better than her on the Quantitative Reasoning section? Round to the nearest whole percent.

f) Explain why simply comparing raw scores from the two sections could lead to an incorrect conclusion as to which section a student did better on.
We cannot compare the raw scores because they are different tests.
We cannot compare the raw scores because we do not have enough information about the other test-takers.
We cannot compare the raw scores because they come from different distributions.
We can compare the raw scores.

Added by Fernando B.

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