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The equation B= 60 x A + 120 can be used to convert scores on standardized...

The equation B= 60 x A + 120 can be used to convert scores on standardized test A to scores on standardized test B. Treat A and B in this equation as random variables. ​a) Suppose a school has a mean score on test A of 25 . What is its equivalent mean score on test​ B? ​b) If one school has a standard deviation of 4 points on test​ A, what is the standard deviation of its equivalent score on test​ B?

math   Statistics-And-Probability   
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Answer #1

a) B= 60 A +120

Given , E(A) = 25

Mean score of B is given by

E(B) = E(60 A +120 )

= 60E(A) + E(120)

= 60*25+120

= 1625

b) Given

then , Var(A) = 42 =16

Variance of B is

Var(B) = Var(60 A +120)

=Var(60 A) +Var(120)

= 602 Var(A) + 0 ( variance of constant term is zero, thus , Var(120)=0 and Var (cX) = c2Var(X) , c is a constant)

= 3600*16

= 57600

Thus standard deviation of B

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