Final answer:
To estimate the number of errors in a chapter of 40 pages with errors per page following a Poisson Distribution with mean μ, the chapter errors also follow a Poisson Distribution with mean 40μ. Calculations can be made using the Poisson PMF with this new mean.
Step-by-step explanation:
To estimate the number of word-processing errors in an entire chapter of a textbook with 40 pages, when the number of errors per page follows a Poisson Distribution with a known mean μ, one can use the properties of the Poisson Distribution. Since each page is independent from the others, the sum of word-processing errors for all 40 pages will also follow a Poisson Distribution. The mean number of errors in the chapter will be 40 times the mean number of errors per page (μ), i.e., μ' = 40μ. In order to calculate probabilities regarding the number of errors in the chapter, you would use the Poisson probability function with this new mean μ'.
The relevant probability distribution for the number of errors in the entire chapter is thus a Poisson Distribution with mean 40μ. For example, if we wish to calculate the probability of finding exactly k errors in the whole chapter, we would use the Poisson probability mass function (PMF): P(X = k) = λ^k * e^(-λ) / k!, where λ is the new mean, 40μ, and k is the number of errors we're interested in.
To find probabilities for different numbers of errors, one would typically use probability distribution tables for the Poisson Distribution or a statistical software that can calculate these values.