Assignment:
The number of violent crimes committed in a large city follows a Poisson distribution with an average rate of 10 per month.
a. Find the expected number of violent crimes committed in a 3 month period
b. Find the standard deviation of the number of violent crimes committed in a 3 month period
c. Find the probability that at least 45 violent crimes will be committed in a 3 month period
d. Find the probability that between 25 and 40 violent crimes will be committed in a 3 month period
e. Find the probability that less than 20 violent crimes will be committed in a 3 month period
Provide complete and step by step solution for the question and show calculations and use formulas.