## Related questions with answers

**Requests to a Web server**. In Exercise $4.175$ (p. 258) 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 $n=60$ Web server requests, let $\bar{x}$ represent the sample mean number of seconds from the start of the hour that the request is made. Find the probability that $\bar{x}$ is between 1,700 and 1,900 seconds.

Solution

VerifiedGiven:

$\begin{align*} n&=\text{Sample size}=60 \end{align*}$

$x$ has a uniform distribution between 0 and 3600.

$\begin{align*} a&=0 \\ b&=3600 \end{align*}$

We need to determine the probability $P(1700<\overline{x}<1900)$.

To derive the probability, the sample means $\overline{x}$ need to be converted to z-scores and then determine the probability using the normal distribution.

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