Question

ACT and SAT scores are both known to be normally distributed. In 2010, the mean and standard deviation for the ACT were μ=21 and σ=7, respectively. The mean and standard deviation for the SAT were μ=1510 and σ=310, respectively. a. What ACT score would place a student in the same percentile as a student who scored 1980 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 1980?) Round your answer to the nearest integer. 34.3 Incorrect: Your answer is incorrect. b. What SAT score would place a student in the sample percentile as a student who scored 10 on the ACT in 2010? (In other words, what SAT score is "equivalent" to an ACT score of 10?) Round your answer to the nearest integer. 1246.5 Incorrect: Your answer is incorrect. c. Suppose Bertrand scored 33 on the ACT in 2010. Which of the following statements below are correct ways of describing his score? Select all that apply. Bertrand's score was about 11.97 standard 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 0.04. About 96% of all students who took the ACT in 2010 scored lower than Bertrand. Bertrand's score was about 0.96 standard 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 0.96. Bertrand's score was about 1.71 standard deviations away from the mean score for everyone who took the ACT in 2010. About 96% of all students who took the ACT in 2010 scored higher than Bertrand.

Answer 1

Ans:

a)

For SAT:

z=(1980-1510)/310=1.52

so,equivalent score for ACT:

x=21+1.52*7=32

b)

For ACT:

z=(10-21)/7=-1.57

Equivalent SAT score:

x=1510-1.57*310=1023

c)

z=(33-21)/7=1.71

P(z<1.71)=0.9568 or 95.68%

Below options are corrrect:

The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.04.

About 96% of all students who took the ACT in 2010 scored lower than Bertrand.

Bertrand's score was about 1.71 standard deviations away from the mean score for everyone who took the ACT in 2010.