Question

Suppose the number of hits a webpage receives follows a Poisson distribution. The average number of hits per minute is 2.4. What is the probability the page will get at least one hit during any given minute?

Answer 1

Answer:

The probability that the page will get at least one hit during any given minute is 0.9093.

Step-by-step explanation:

Let X = number of hits a web page receives per minute.

The random variable X follows a Poisson distribution with parameter,

λ = 2.4.

The probability function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...$

Compute the probability that the page will get at least one hit during any given minute as follows:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

             $=1-\frac{e^{-2.4}(2.4)^{0}}{0!}\\=1-\frac{0.09072\times1}{1} \\=1-0.09072\\=0.90928\\\approx0.9093$

Thus, the probability that the page will get at least one hit during any given minute is 0.9093.