
Poisson Probability
The average number of calls received by a switchboard in a 30minute 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 probabilitythat between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?
Not really Sure how to set up.

The Poisson Probability Distribution is very straightforward. Simply calculate the desired values.
$\displaystyle Pr(n = 10)\;=\;e^{10}*\frac{10^{10}}{10!}\;=\;0.125$
As long as we are sticking witht he halfhour period already defined, just go with it. No adjustment is required.
$\displaystyle Pr(9\;<\;n\;<\;15)\;=\;e^{10}*\sum_{n=10}^{14}\left(\frac{10^{n}}{n!}\right) \;=\;0.459$
You do the last one.