# Math Help - Poisson Probability

1. ## Poisson Probability

The average number of calls received by a switchboard in a 30-minute period is 15

a. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls?
b. What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls?
c What is the probability-that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?

Not really Sure how to set up.

2. The Poisson Probability Distribution is very straight-forward. Simply calculate the desired values.

$Pr(n = 10)\;=\;e^{-10}*\frac{10^{10}}{10!}\;=\;0.125$

As long as we are sticking witht he half-hour period already defined, just go with it. No adjustment is required.

$Pr(9\;<\;n\;<\;15)\;=\;e^{-10}*\sum_{n=10}^{14}\left(\frac{10^{n}}{n!}\right) \;=\;0.459$

You do the last one.