Question

The customer's arrival at a bank is random and independent; the probability of an arrival in any one minute lapse is the same probability of an arrival in another lapse of a minute. Answer the questions that follow. (Poisson)

What is the probability of exactly 4 arrivals in a minute?

What is the probability of at least 4 arrivals in one minute?

please write legible

Answer 1

(a)

Probability Mass Function of Poisson Distribution with = 1 is given by:

,

        for x = 0, 1, 2,..

For X = 4, we get:

(b)
P(X4) =1 - [P(X=0)+P(X=1)+P(X=2)+P(X=3)]

So,

P(X4) = 1 - 0.9810

          = 0.0190

So,

Answer is:

0.0190