The number of calls for service utilizing the 911 system received by the Cape Coral Police Department on a Saturday night is 20 calls per hour and follows a Poisson distribution.
a. Find the mean and standard deviation for the number of calls between midnight and 3 am.
If the number of calls exceeds 30 per hour, then lower priority calls may not receive police follow-up in a timely manner.
b. Find the probability that no more than 30 calls are received during any given hour on Saturday night.
c. What is the probability over the course of a twelve hour shift that there will be at least one hour in which follow-up is not timely?
The inter-arrival time between calls is the length of time between the receipt of one call and the next.
d. Find the probability that the inter-arrival time between two consecutive calls is between 1 and 2 minutes.