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.