In a book, 2 misprints occur per 100 pages. Using the cumulative Poisson probability table available in your text, we can determine which of the following probabilities in a book of 500 pages?
A) The probability of finding between 5 and 6 misprints equals .099.
B) The probability of finding at least 20 misprints equals .003.
C) The probability of finding at least 24 misprints equals .1234.
D) The probability of finding at least 20 misprints equals 1.
E) The probability of finding at least 24misprints equals 1.

Question

Quizplus · Accepted Answer

Given that there are 2 misprints per 100 pages, in a 500-page book, we would expect 10 misprints (2 misprints/100 pages * 500 pages). The Poisson distribution is used for calculating the probability of a given number of events happening in a fixed interval of time or space if these events happen with a known constant rate and independently of the time since the last event. The probability of finding at least 20 misprints is very low given the expected number is 10, making option B the most plausible among the given choices, as it suggests a very low probability (.003) for a significantly higher number of misprints than expected. Options involving probabilities of 1 for finding at least 20 or 24 misprints are incorrect because the probability of such high deviations from the mean is not 1 but significantly lower, reflecting the rare nature of such occurrences in a Poisson distribution.

In a Book, 2 Misprints Occur Per 100 Pages