Probability Distribution help fast

[tanmaydube]

Exam marks, X, have mean 70 and standard deviation 8.7. The marks need to be scaled using the formula Y = aX +b so that the scaled marks, Y, have mean 55 and standard deviation 6.96.
Find the values of a and b.(ans: a=0.8 and b=1)

thank you for helping!

 

[Moiz]

Y=aX+b
so E(Y)= a E(X) + b
=> 55 = 70a + b

Var(Y)= a^2 Var(X)
=> (6.96)^2 = a^2 (8.7)^2
=> a^2 = 0.64
=> a= 0.8

b= 55 - 70 ( 0.8 )
b= -1