Calls to the customer service department of a cable TV provider are made randoml

Question

Calls to the customer service department of a cable TV provider are made randomly and independently at a rate of 11 perminute. The company has a staff of 20 customer service specialits who handle all the calls. Assume that none of the specialists are on a call at this moment and that a Poisson model is appropriate for the number of incoming calls per minute.

(a) What is the probability of the customer service department receiving more than 20 calls in the next minute?

(b) What is the probability of the customer service department receiving exactly 20 calls in the next minute?

(c) What is the probability of the customer service department receiving fewer than 11 calls in the next minute?

Thanks.

Explanation / Answer

Poisson's Distribution Formula:
P(X = x) = (e^-)*(^x) / x!

here = 11

a)
P(X > 20) = 0.00467
In order to do this calculation we have to use advanced calculator. Excel formula used: =1-POISSON.DIST(20,11,TRUE)

b)
P(X = 20) = (e^-11)*(11^20) / 20! = 0.00462

c)
P(X < 11) = 0.5401
In order to do this calculation we have to use advanced calculator. Excel formula used: =1-POISSON.DIST(10,11,TRUE)

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