The annual number of industrial accidents occurring in a particular manufacturing plant is known to follow a Poisson distribution with mean 12.
a. What is the probability of observing exactly 12 accidents during the coming year?
b. What is the probability of observing no more than 12 accidents during the coming year?
c. What is the probability of observing at least 15 accidents during the coming year?
d. What is the probability of observing between 10 and 15 accidents (inclusive) during the coming year? e. Find the smallest integer k such that we can be at least 99% sure that the annual number of accidents occurring will be less than k.