Requests to a Web server. In Exercise 5.10

(p. 266) you learned that Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution. Specifically, the number of seconds x from the start of the hour that the request is made is uniformly distributed between 0 and 3,600 seconds. In a random sample of n = 75 Web server requests, let x represent the sample mean number of seconds from the start of the hour that the request is made.

a. Find E1x2 and interpret its value.

b. Find Var(x).

c. Describe the shape of the sampling distribution of x.

d. Find the probability that x is between 1,900 and 1,950 seconds.

e. Find the probability that x exceeds 2,150 seconds..