Question

Suppose a representative at a credit card customer service center receives a phone call every 5 minutes on average.

(a) Find the probability that she receives 3 phone calls in 20 minutes?
(b) Find the probability that she receives less than 3 phone calls in 20 minutes?
(c) Find the expected number of phone calls she receives in 20 minutes?

Answer 1

Answer: a) probability = 0.195

b) probability = 0.2381

c) expected number = 4

Explanation:

Let X be a random variable which shows the number of calls in 20 minutes. Since credit card customer service center receives a phone call every 5 minutes on average, given X has Poisson distribution with parameter λ = (1/5)*20 = 4 call per 20 minutes.

Given that t = 20

a)

The probability that she receives 3 phone calls in 20 minutes is

P(X=3) = [ e∧-λt (λt)3 ] / 3ḷ

P(X-3) = [e∧-20/5 (20/5)3] / 3ḷ = 0.195

b)

The probability that she receives fewer than 3 phone calls in 20 minutes is

P(X˂3) = ∑_(x=0)^2▒ (e∧-4×4x) / xḷ = 0.2381

c)

The expected number of phone calls she receives in 20 minutes is

E(X) = λ = 4

i.e.

λ = 1/5 * 20 = 4