Quote:

2) The inside diameter of a cylindar tube is a random variable X w. mean of 3 in and a S.D. of 0.2 in and the thickness of the tube is a random variable Y w. the mean of 0.3 in and the S.D. of .005 the two random variables are independent Find the mean and the standard deviation of the outside diameter Z=X+2Y

to get the SD I take equation and put the S.D. in so i will get (0.2)^2+2(0.005)^2 then I take the answer that I get and take the Square root to get the new standard. How do I find the mean?

Any help is apprieciated. Thank you for your time.

Z is the sum of two independent normaly distributed random variables, so