Question

# Telephone calls arrive at a 911 call center at the rate of 12 calls per hour....

Telephone calls arrive at a 911 call center at the rate of 12 calls per hour.

What is the mean number of calls the center expects to receive in 30 minutes?

What is the standard deviation of the number of calls the center expects to receive in 30 minutes? (Round your answer to two decimal places.)

Find the probability that no calls come in for 30 minutes. (Round your answer to five decimal places.)

Poisson distribution is used to model rate of random events that occur (arrive) in some fixed time interval.

Given :

12 calls per hour

Average number of calls in 30 minutes

The mean number of calls the center expects to receive in 30 minutes is 6

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Standard deviation =

The standard deviation of the number of calls the center expects to receive in 30 minutes is 2.45

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P ( no calls come in for 30 minutes ) = P(X=0)

The probability formula for poisson distribution is

now plug the values in the formula ,

The probability that no calls come in for 30 minutes is 0.00248

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