Question

A radio station is looking for the 90th​​ caller to win the grand prize of a year’s tuition to the winner’s desired program at the local university. The total new calls arrive as a (λA=10/minute)-Poisson process and each call takes an average of 10 seconds to process.

Assume the line is free when the contest starts and calls that arrive while another call is being processed are dropped.

What is the expected time that the radio station will have to wait to award their grand prize?

Answer 1

Solution :-

Here we need to find out the  expected time that the radio station will have to wait to award their grand prize.

Now consider the total time for a call to process.

we know that,  total time for a call to process = arrival time + call time.

From given data, total time for a call to process = (60/10) +10

= 6 + 10

= 16 minutes.

Hence, total time for a call to process = 16 minutes.

Then, Expected time = 90 * 16

Expected time = 1440 seconds

Expected time = 1440 / 60 minutes

Expected time = 24 minutes.

Hence, Expected time that the radio station will have to wait to award their grand prize = 24 minutes.