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?

a) probability = 0.195

b) probability = 0.2381

c) expected number = 4

Step-by-step 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

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1