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

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.