Question

the number of hits to a website follows a poisson process. hits occur at the rate of 0.2 per minute between 7:00 p.m. and 9:00 p.m. given below are three scenarios for the number of hits to the website. compute the probability of each scenario between 8:38 p.m. and 8:44 p.m. interpret each result.
(a) exactly four
(b) fewer than four
(c) at least four

(a) ( p(4)=0.0260 )
(round to four decimal places as needed.)
on about 3 of every 100 time intervals between 8:38 p.m. and 8:44 p.m, the website will receive exactly 4 hit(s).
(round to the nearest whole number as needed.)
(b) ( p(x < 4)=0.9663 )
(round to four decimal places as needed.)
on about of every 100 time intervals between 8:38 p.m. and 8:44 p.m, the website will receive hit(s).
(round to the nearest whole number as needed.)

Explanation:

Step1: Understand the probability value

We are given \(P(x < 4)=0.9663\). This means the probability that the number of hits \(x\) is less than 4 in the given time - interval.

Step2: Calculate the number of intervals

To find the number of intervals out of 100, we use the formula \(n = P\times100\). Substituting \(P = 0.9663\), we get \(n=0.9663\times100 = 96.63\).

Step3: Round the number

Rounding \(96.63\) to the nearest whole number. Since the decimal part \(0.63\gt0.5\), we round up.

Answer:

On about \(97\) of every 100 time intervals between 8:38 P.M. and 8:44 P.M, the website will receive fewer than \(4\) hit(s).