ACT and SAT scores are both known to be normally distributed. In 2010, the mean

Question

ACT and SAT scores are both known to be normally distributed. In 2010, the mean and standard deviation for the ACT were -21 and -7, respectively. The mean and standard deviation for the SAT were -1510 and 310, respectively. a. What ACT score would place a student in the same percentile as a student who scored 2230 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 22307) Round your answer to the nearest integer. b. What SAT score would place a student in the sample percentile as a student who scored 19 on the ACT in 2010? (In other words, what SAT score is "equivalent" to an ACT score of 19?) Round your answer to the nearest integer. c. Suppose Bertrand scored 35 on the ACT in 2010. Which of the following statements below are correct ways of describing his score? Select all that apply. O The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.98 About 98% of all students who took the ACT in 2010 scored higher than Bertrand. Bertrand's score was about 2.00 standard deviations away from the mean score for everyone who took the ACT in 2010 O About 98% of all students who took the ACT in 2010 scored lower than Bertrand. Bertrand's score was about 14 standard deviations away from the mean score for everyone who took the ACT in 2010 Bertrand's score was about 0.98stadard deviations away from the mean score for everyone who took the ACT in 2010 The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.02

Explanation / Answer

Z = (X - mean)/standard deviation

a) Z score corresponding to SAT score of 2230 = (2230 - 1510)/310 = 2.323

ACT score equivalent = 2.323x7 + 21 = 37

b) Z score corresponding to ACT score of 19 = (19 - 21)/7 = -0.286

SAT score equivalent = -0.286x310 + 1510 = 1421

c) Z score of Bertrand = (35-21)/7 = 2

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