Question

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.

What is the expected number of calls in one hour?

Answer 1

Let X the random variable who represent the number of occurences in a period of time for the calls.

For this case we have the following parameter
`\lambda = 1 (call)/(2 minutes)`

And we are interested in the expected number of calls in one hour.

We know that 1 hr = 60 mins so then the expected number of calls that arrive in one hour are:

`\lambda = (1 call)/(2 minutes) * (60 minutes)/(1 hour) = 30 calls per hour`

Explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

`P(X=x) =\lambda^x (e^(-\lambda))/(x!)`

And the parameter
`\lambda` represent the average ocurrence rate per unit of time.

Solution to the problem

Let X the random variable who represent the number of occurences in a period of time for the calls.

For this case we have the following parameter
`\lambda = 1 (call)/(2 minutes)`

And we are interested in the expected number of calls in one hour.

We know that 1 hr = 60 mins so then the expected number of calls that arrive in one hour are:

`\lambda = (1 call)/(2 minutes) * (60 minutes)/(1 hour) = 30 calls per hour`