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

Answer:

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 $\lambda = 1 \frac{call}{2 minutes}$

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:

$\lambda = \frac{1 call}{2 minutes} * \frac{60 minutes}{1 hour} = 30 calls per hour$

Step-by-step 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:

$P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}$

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 $\lambda = 1 \frac{call}{2 minutes}$

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:

$\lambda = \frac{1 call}{2 minutes} * \frac{60 minutes}{1 hour} = 30 calls per hour$