Server A sequentially handles 30 jobs, each of whose service times are i. i.d. (independent, identically distributed) a continuous random variable with mean 50 milliseconds and a standard deviation of 10 milliseconds. Server B has an analogous workload, but its 30 jobs each have mean 52 milliseconds and standard deviation 15 milliseconds a. Estimate the probability that server A finishes in less than 3980 milliseconds.
b. Estimate the probability that server B finishes in less than 3980 milliseconds.
c. Suppose that the two random variables Xi ~ N( i,Æ¡?), for i E {1,2}, are independent. What is EX1-X2)? What is Var(X-%)?
d. Estimate the probability that server B finishes before A. You may use without proof the fact that, if X1 and X2 are independent normal random variables, then aXi + bX2 is also normal, for any constants a and b (and that the analogous statement holds for random variables that are approximately normal)
e. If you did part (d) correctly, you will discover that B has a nonnegligible chance of finishing earlier than A, even though A has the smaller mean completion time. Explain how this is possible.