Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be?

Name: Solved: Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be? - MathMaster
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Answer to a math question Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be?

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92 Answers

E(a+bX)=75

E(a)+bE(X)=75

a+70b=75

70b=75-a and Var(a+bX)=12^2

b^2Var(X)=144

b^2(15)^2=144

b^2=\frac{144}{225}

b=\frac{12}{15}

b=\frac{4}{5} then 70b=75-a

56=75-a

a=19 therefore, a=19 and b=\frac{4}{5}

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