Question

You are manager of a ticket agency that sells concert tickets. You assume that people will call 4 times in an attempt to buy tickets and then give up. Each telephone ticket agent is available to receive a call with probability 0.25. If all agents are busy when someone calls, the caller hears a busy signal.

Find n, the minimum number of agents that you have to hire to meet your goal of serving 95% of the customers calling to buy tickets.

Answer 1

We are given,  

Each telephone ticket agent is available to receive a call with probability 0.25

So the probability that telephone ticket agent is not available to receive a call is 1 - 0.25 = 0.75

The people will call 4 times in an attempt to buy tickets and then give up.

So the probability that a caller / buyer fails to get through in 4 tries is

Let there are n number of agents.

An attempt is a failure if all n operators are busy,with probability

  **....*n times

=

You have to serve at least 95% of the customers calling to buy tickets.

That is less than or equal to 5% of the customers fails to buy tickets.

So probability statement would be   0.05

taking log on both sides,

4n LN(0.75) LN(0.05)

4n

4n = = 10.4133

4n = 10.4133

n = 10.4133 / 4

n = 2.60 3

So there should be 3 number of agents that you have to hire to meet your goal of serving 95% of the customers calling to buy tickets.