Suppose that X is a random variable with mean 30 and standard deviation 10. Also suppose that Y is a random variable with mean 20 and standard deviation 8. Assume that the correlation between X and Y is 0.4. Find the mean and standard deviation of the random variable Z for each of the following cases. Be sure to show your work. a. Z = 2 + 10X. b. Z = X + Y. c. Z = - 5X - 3Y

Part a: For variable X using z score you have (x-30) / 10, replace X for this expression in (a), i mean Z=2+10 ((x-30) / 10) = 2+x-30 = put this in the way of z score = (x-18) / 1, so the mean is 18 and standard deviation is 1.

Part b: Z=X+Y = (x-30) / 10 + (x-20) / 8 = solve adding fractions = (18x-440) / 80 now divide all the numbers between 18 (because you need to show as z score way) = (x-24.4) / 4.4, so the mean is 24.4 and standard deviation is 4.4.

For part c, do the same.