The calls coming into a call center follow a Poisson distribution, and have a st

Question

The calls coming into a call center follow a Poisson distribution, and have a standard deviation of 0.6 calls per minute.

(a) What is the probability the call center gets 4 calls in the next 8 minutes.

(b) Let Y be the number of calls they receive in the next 15 minutes. Find the moment generating function.

(c) Find the probability that the time between the last call and the next call will be between 1 to 4 minutes.

(d) Find the probability that the fifteenth minute after the start of a shift will be the fifth minute that the center receives exactly one call.

(e) Let X be the time until the center receives its third call. Find P(X<5).

Explanation / Answer

Mean = 0.6^2 = 0.36

SD = 0.6

P(X<=8) = sumx:0 to 8 [ e^(-0.36) 0.36^x / x!]

e) P(X<5) = sumx:0 to 4 [ e^(-0.36) 0.36^x / x!]

c) P(1<=X<=4) = P(X<=4) - P(X<1) = sumx:0 to 4 [ e^(-0.36) 0.36^x / x!] - e^(-0.36)

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