The probability that one randomly selected student who took the ACT in 2010 scor

Question

The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.16.Bertrand's score was about 1.00 standard deviations away from the mean score for everyone who took the ACT in 2010.Bertrand's score was about 0.84 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 0.84.About 84% of all students who took the ACT in 2010 scored lower than Bertrand.Bertrand's score was about 7 standard deviations away from the mean score for everyone who took the ACT in 2010.About 84% of all students who took the ACT in 2010 scored higher than Bertrand.

10. 5 points My Notes 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 2020 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 2020?) Round your answer to the nearest integer b. What SAT score would place a student in the sample percentile as a student who scored 16 on the ACT in 2010? (In other words, what SAT score is "equivalent to an ACT score of 16?) Round your answer to the nearest integer c. Suppose Bertrand scored 28 on the ACT in 2010. Which of the following statements below are correct ways of describing his score? Select all that apply. The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.16 Bertrand's score was about 1.00 standard deviations away from the mean score for everyone who took the ACT in 2010 Bertrand's score was about 0.84 standard deviations away from the mean score for everyone who took the ACT in 2010 O The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.84. About 84% of all students who took the ACT in 2010 scored lower than Bertrand. Bertrand's score was about 7 standard deviations away from the mean score for everyone who took the ACT in 2010 About 84% of all students who took the ACT in 2010 scored higher than Bertrand Submit Answer Save Progress Practice Another Version Viewing Saved Work Revert to Last Response

Explanation / Answer

Ans:

a)

For SAT:

z=(2020-1510)/310=1.645

so,equivalent score for ACT:

x=21+1.645*7=33

b)

For ACT:

z=(16-21)/7=-0.714

Equivalent SAT score:

x=1510-0.714*310=1289

c)

z=(28-21)/7=1

P(z<1)=0.8413 or 84.13%

below options are corrrect:

The probability that one randomly selected student who took the ACT in 2010 scored higher than Bertrand is about 0.16.

Bertrand's score was about 1.00 standard deviations away/above from the mean score for everyone who took the ACT in 2010.

About 84% of all students who took the ACT in 2010 scored lower than Bertrand.

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