A retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is three per week. Let x denote the number of bad checks cashed per week. Assuming that x has a Poisson distribution:
a. Find the probability that the store's cashiers will not cash any bad checks in a particular week.
b. Find the probability that the store will meet its goal during a particular week.
c. Find the probability that the store will not meet its goal during a particular week.
d. Find the probability that the store's cashiers will cash no more than 10 bad checks per two-week period.
e. Find the probability that the store's cashiers will cash no more than five bad checks per three-week period.