Question

question: Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the website is 2.7 per hour. Complete parts​ (a) through​ (d) below.

A) What is the probability that in any given hour zero new visitors will arrive at the​ website?

The probability that zero new visitors will arrive is___

b. What is the probability that in any given hour exactly one new visitor will arrive at the​ website?

The probability that exactly one new visitor will arrive is____

c. What is the probability that in any given hour two or more new visitors will arrive at the​ website?

The probability that two or more new visitors will arrive is____

d. What is the probability that in any given hour fewer than three new visitors will arrive at the​ website?

The probability that fewer than three new visitors will arrive is____

Answer 1

this is Poisson distribution with parameter λ =2.6

a)

probability =

P(X=0)=

{e-λ*λx/x!}=

0.0743

b)

probability =

P(X=1)=

{e-λ*λx/x!}=

0.1931

c)

probability that in any given hour two or more new visitors will arrive at the​ website=P(X>=2)=1-P(X<=1)

=1-((P(X=0)+P(X=1))=1-(0.0743+0.1931)=0.7326

d)

probability that in any given hour fewer than three new visitors will arrive at the​ website =P(X<3)

=P(X=0)+P(X=1)+P(X=2)=0.5184