Requests to a Web server. Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution (see Example 4.27). 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. It can be shown that the distribution of x has mean m = 1,800 and variance s2 = 1,080,000. In a random sample of n = 60 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 1,700 and 1,900 seconds.

e. Find the probability that x exceeds 2,000 seconds.
Applying the Concepts—Intermediate