Step 1 :The problem involves finding probabilities related to the number of typographical errors on a page. The mean number of errors is given as 8. This is a Poisson distribution problem because we are dealing with the number of events (errors) that occur in a fixed interval (a page).
Step 2 :The Poisson probability formula is given by: \(P(x; μ) = (e^-μ) * (μ^x) / x!\) where: \(P(x; μ)\) is the Poisson probability, x is the actual number of successes, e is approximately equal to 2.71828, μ is the mean number of successes, and x! is the factorial of x.
Step 3 :For part (a), we need to find the probability of exactly 5 errors. We can plug x=5 and μ=8 into the Poisson formula. The calculated probability is approximately 0.0916.
Step 4 :For part (b), 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. The calculated probability is approximately 0.1912.
Step 5 :For part (c), we need to find the probability of more than 5 errors. This is 1 minus the probability of at most 5 errors. The calculated probability is approximately 0.8088.
Step 6 :Final Answer: \(\boxed{0.8088}\) (Round to four decimal places as needed.)