The Poisson Probability Distribution is very straight-forward. Simply calculate the desired values.
As long as we are sticking witht he half-hour period already defined, just go with it. No adjustment is required.
You do the last one.
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.