Mean and standard deviation for linear combinations

[engineer23]

Homework Statement

Data set in X with mean xbar = 100 and standard deviation Sx = 10

Find ybar and Sy for 2(Yi-5)/10 + 7

Homework Equations

The Attempt at a Solution

All the problems I have seen are in the form yi = axi + b in which case the mean ybar = a(xbar) + b and Sy = aSx

What does Yi represent exactly? How does it relate to xi?

 

[Mark44]

I don't see how you can find ybar and Sy unless you know the relationship between X and Y.

You show an expression 2(Y_i - 5)/10 + 7 = (Y_i - 5)/5 + 7. Could this be X_i?

If that's the case, then you can solve for Y_i.

X_i = (Y_i - 5)/5 + 7
==> X_i - 7 = (Y_i - 5)/5
==> 5(X_i - 7) = (Y_i - 5)
==> 5(X_i - 7) + 5 = Y_i
or
Y_i = 5X_i - 30