.
If calls to your cell phone are a Poisson process with a constant rate =2 calls per hour,
what’s the probability that, if you forget to turn your phone off in a 1.5 hour movie,
your phone rings during that time?
~~~~~~~~~~~~~~~~
From the "given" part, we know the following:
- The Poisson random variable is 1 (we are focused on getting at least ONE phone call).
- The average rate of success in this particular time interval of 1.5 hours
is 2 phone calls multiplied by 1.5 hours, i.e. 2*1.5 = 3 phone calls per time period of 1.5 hours.
Here we define a "success" as the phone ringing.
Since the phone rings two times per hour (as average; given), the average rate of phone ringing
is 2*1.5 = 3 times per this particular time period of 1.5 hours.
Use free of charge online calculator of the Poisson Probability
https://stattrek.com/online-calculator/poisson.aspx
Plug those numbers into the Poisson Calculator and hit the Calculate button.
The calculator reports that the cumulative Poisson probability is 0.95021. ANSWER
That is the cumulative probability of getting at least one phone call in 1.5 hours.
Solved and carefully explained.