Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is eight. Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typographical errors are found on a page. (c) $P$ (more than five typographical errors are found on a page $)=0.8088$ (Round to four decimal places as needed.) Which of the events are unusual? Select all that apply. A. The event in part (a) is unusual. B. The event in part (b) is unusual. C. The event in part (c) is unusual. D. None of the events are unusual.

Step 1 ：The problem involves a Poisson distribution, as it deals with the number of events (typographical errors) occurring within a fixed interval (a page). The mean number of errors per page is given as 8. We are asked to find the probability of exactly 5 errors, at most 5 errors, and more than 5 errors.

Step 2 ：For the first part of the question, we need to find the probability of exactly 5 errors. The formula for the Poisson distribution is: \(P(X=k) = \frac{λ^k * e^-λ}{k!}\) where λ is the mean number of events, k is the actual number of events, and e is the base of the natural logarithm.

Step 3 ：For the second part, we need to find the probability of at most 5 errors. This is the sum of the probabilities of 0, 1, 2, 3, 4, and 5 errors.

Step 4 ：For the third part, we need to find the probability of more than 5 errors. This is 1 minus the probability of at most 5 errors.

Step 5 ：An event is considered unusual if its probability is less than or equal to 0.05.

Step 6 ：The probabilities of exactly five typographical errors, at most five typographical errors, and more than five typographical errors are approximately 0.0916, 0.1912, and 0.8088, respectively.

Step 7 ：None of the events are unusual. Therefore, the answer is \(\boxed{D}\).