The average number of meteorites striking the earth in a week is 119, and you may assume that this follows a poisson distribution.
(a) What is the probability that on a given day, either 15 or 16 meteorites strike the earth? Leave your final answer to 4 decimal places.
(b) By approximating the poisson distribution to a binomial distribution, state the binomial distribution which reflects the same problem in (a). Each interval in the binomial distribution represents 1 hour. Leave your final answer to 4 decimal places.
(c) Hence, using your binomial distribution in (b), find the probability that on a given day, either 15 or 16 meteorites strike the earth. Leave your final answer to 3 decimal places.
(d) Is your binomial distribution a good approximation of the poisson distribution in this case? Briefly explain why or why not. If applicable, provide a possible solution such that a binomial distribution will be a good approximation of the poisson distribution in this case.