Question

Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 640 on the Verbal Reasoning section and 740 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 461 with a standard deviation of 107, and the mean score for the Quantitative Reasoning was 450 with a standard deviation of 147. Suppose that both distributions are nearly normal. Round calculated answers to 4 decimal places unless directed otherwise.

1.Write down the short-hand for these two normal distributions.

2. What is her Z score on the Verbal Reasoning section?

3. What is her Z score on the Quantitative Reasoning section?

4.Relative to others, which section did she do better on? A. Quantitative Reasoning B. She did the same on both sections C. Verbal Reasoning

5. What is her percentile score on the Verbal Reasoning section? Round to nearest whole number.

6. What is her percentile score on the Quantitative Reasoning section? Round to nearest whole number.

7. What percent of the test takers did better than she did on the Verbal Reasoning section? %

8. What percent of the test takers did better than she did on the Quantitative Reasoning section? %

9. What is the score of a student who scored in the 68?ℎ percentile on the Quantitative Reasoning section? Round to the nearest integer.

10. What is the score of a student who scored worse than 88% of the test takers in the Verbal Reasoning section? Round to the nearest integer.

Only need 5-10

Answer #1

1) Verbal Reasoning section ~N(461,107)

Quantitative Reasoning section~ N(450,147)

2) Z score =(640-461)/107 =1.6729

3)z score =

4)

A. Quantitative Reasoning

5)

probability =P(X<640)=(Z<640-461)/107)=P(Z<(1.6729)=0.9528~ 95 |

6)

probability =P(X<740)=(Z<740-450)/147)=P(Z<(1.9728)=0.9757~ 98 |

7) 100-95 =5 %

8)100-98 =2 %

9)

for 68th percentile critical value of z= | 0.468 | ||

therefore corresponding value=mean+z*std deviation= | 518.7517 |

10)

for 12th percentile critical value of z= | -1.175 | ||

therefore corresponding value=mean+z*std deviation= |
335.2764 |

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