Phone calls are received at Janice’s house according to a Poisson Process with parameter λ=2 per hour.

How long can Janice’s shower be if she wishes the probability of receiving no phone calls to be at most 0.5?

What I have tried: Substituted λt in the poisson formula with x = 0 which should be less than 0.5. Should I be taking log on both sides?

The answer is 20 minutes - how?

  • $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Please add the [self-study] tag and read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ – jbowman Sep 9 '18 at 18:03
  • $\begingroup$ @jbowman Not my homework, it is entirely for self-study. Will try and show what I have done till now. $\endgroup$ – user218970 Sep 9 '18 at 18:04
  • $\begingroup$ My apologies, we get a lot of "please do my homework for me" questions. I'll modify my standard text to take into account the possibility that it really is self-study. $\endgroup$ – jbowman Sep 9 '18 at 18:06
  • $\begingroup$ @jbowman Thank you so much for being considerate. I'm sorry for not adding my attempt at solving this question into the post. $\endgroup$ – user218970 Sep 9 '18 at 18:08
  • $\begingroup$ So you have something of the form $\exp\{-2t\} \leq 0.5$? $\endgroup$ – jbowman Sep 9 '18 at 18:10

$ P(J) = \frac{e^{-2t}(2)^0}{0!} ≤ 0.5 $

Take Log on both sides:

-2t = -0.69

From here solving for t is easy. The answer should be around 20.79 minutes which you can round to 20 minutes.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy