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Sagan scored 1200 on the SAT. The distribution of SAT scores in a reference population is...

Sagan scored 1200 on the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 980 and standard deviation 100. Andrea scored 27 on the ACT. The distribution of ACT scores in a reference population is normally distributed with mean 20 and standard deviation 5. Who performed better on the standardized exams and why?

a. Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.

b. Sagan scored higher than Andrea. Sagan's score was a 1200, which is greater than Andrea's score of 27.

c. Andrea scored higher than Sagan. Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean, but closer to the mean than Sagan's standardized score of 2.2 standard deviations above the mean.

d. Sagan scored higher than Andrea. Sagan's score was 220 points above the mean of 980, and Andrea's was 7 points above the mean of 20.

e. Andrea scored higher than Sagan. Andrea is only 9 points from the top score of 36 on the ACT, and Sagan is 400 points from the top score of 1600 on the SAT.

Math   Statistics-And-Probability   
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Answer #1

Option A is correct.

Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.

Mean = 980

Standard deviation = 100

Given Sagan scored 1200 on the SAT

P(X = 1200) = (1200-980)/100

= 220/100= 2.2

Now Andrea scored 27 on ACT.

P(X = 27) = (27-20)/5

= 7/5= 1.4

Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.

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