Question

Suppose that incoming calls per hour to an agent of a customer service center of a small credit union are uniformly distributed between 0 and 6 calls. If the center has 10 independent agents, what is the expected number of agents who receive between 2 and 5 calls

Answer 1

Answer:

The expected number of agents who receive between 2 and 5 calls is 5.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, d greater than c, is given by the following formula.

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

Uniformly distributed between 0 and 6 calls.

This means that $a = 0, b = 6$

Percentage of agents who receive between 2 and 5 calls.

$P(2 \leq X \leq 5) = \frac{5-2}{6-0} = 0.5$

If the center has 10 independent agents, what is the expected number of agents who receive between 2 and 5 calls

Independent, each one with a 0.5 probability. So

10*0.5 = 5

The expected number of agents who receive between 2 and 5 calls is 5.