SOLUTION: In 2005, the mean score on the verbal portion of the SAT for college-bound seniors was 508 with a standard deviation of 113. Assume the test scores are normally distributed. a.

Question 934559: In 2005, the mean score on the verbal portion of the SAT for college-bound seniors was 508 with a standard deviation of 113. Assume the test scores are normally distributed.
a. What percent of the SAT verbal scores are less than 590?
b. If 1200 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) calculate z-score for 590
z-score = (590 - 508) / 113 = 0.725663717 approx 0.73
Pr(X<590) = 0.7673
b) Pr(X>525) = 1 - Pr(X<525)
calculate the z-score for 525
note that the sample size is 1200 > 40, so we can use the population standard deviation
z-score = (525 - 508) / 113 = 0.150442478 approx 0.15
Pr(X>525) = 1 - Pr(X<525) = 1 - 0.5596 = 0.4404

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