Question

The following exercise is best solved with a computer
Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week.

Required:
a. Find the probability that the site gets 10 or more hits in a week.
b. Determine the probability that the site gets 20 or more hits in 2 weeks.

Answer 1

Answer:

(a) The probability that the site gets 10 or more hits in a week is 0.0137.

(b) The probability that the site gets 20 or more hits in 2 weeks is 0.0016.

Step-by-step explanation:

Let X represent the number of hits on a personal website in a week.

It is provided that the hits occur randomly and independently with an average of five per week.

So, X follows a Poisson distribution with parameter λ = 5.

(a)

Compute the probability that the site gets 10 or more hits in a week as follows:

Use Excel.

$P(X\geq 10)=1-P(X<10)$

                 $=1-\sum\limits^{9}_{0}{\frac{e^{-\lambda}\cdot(-\lambda)^{x}}{x!}}\\\\=1-(=\text{POISSON.DIST(10,5,TRUE)})\\\\=1-0.9863\\\\=0.0137$

Thus, the probability that the site gets 10 or more hits in a week is 0.0137.

(b)

Compute the probability that the site gets 20 or more hits in 2 weeks as follows:

In one week the average number of hits was 5.

Then in two weeks the average number of hits will be 10.

$P(X\geq 20)=1-P(X<20)$

                 $=1-\sum\limits^{19}_{0}{\frac{e^{-\lambda}\cdot(-\lambda)^{x}}{x!}}\\\\=1-(=\text{POISSON.DIST(20,10,TRUE)})\\\\=1-0.9984\\\\=0.0016$

Thus, the probability that the site gets 20 or more hits in 2 weeks is 0.0016.