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

2.3

2.3 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____

​(Round to four decimal places as​ needed.)

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____

​(Round to four decimal places as​ needed.)

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____

​(Round to four decimal places as​ needed.)

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 ____

​(Round to four decimal places as​ needed.)

Answer 1

X ~ poi ( )

Where = 2.3

Poisson probability distribution is

P(X) = e^-X / X!

a)

P(X = 0) = e^-2.3

= 0.1003

b)

P(X = 1) = e^-2.3 * 2.3

= 0.2306

c)

P(X >= 2) = 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [ e^-2.3 + e^-2.3 * 2.3]

= 0.6691

d)

P(X < 3) = P(X <= 2)

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

= e^-2.3 + e^-2.3 * 2.3 + e^-2.3 * 2.3² / 2!

= 0.5960