Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 4 and a standard deviation of 1.3; Y has an expected value of 6 and a standard deviation of 0.8; Z has an expected value of -8 and a standard deviation of 0.5 Let T = 2X + 4Y + 42 Variable X Y Z Mean(Expected Value) 4 6 >8 Standard Deviation 1.3 0.8 0.5 Coefficient 2 4 4 a) What is the probability that x > 2? E b) What is the expected value of T? :] c) What is the variance of T? 1:] d) What is the standard deviation of T? :] e) What ls the probability that T is within 0.8 standard deviations of its mean? E f) What is the probability that T is > 8? E 9) What is the probability that T is 0? :] I) Copy your R script or any other comments for the above into the text box here