A radio station is looking for the 90^{th} t h caller to win the grand prize of

Question

A radio station is looking for the 90^{th}th 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 (lambda _{A}=10/A=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?

Explanation / Answer

total time for a call to process =arrival time +call time =(60/10)+10 =16 seconds

hence total time to process 90 calls =16*90=1440 seconds =24 minutes

please reply for doubt

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.