Question

The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or fewer errors in 100 pages?

   The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or fewer errors in 100 pages?

Applied Statistics and Probability for Engineers

Applied Statistics and Probability for Engineers

Douglas C.… 6th Edition

Chapter 3, Problem 192

Instant Answer

Solved by Expert Sonam Khatri

08/10/2021

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01 error per page. We denote this as $X$ and the mean as $\lambda = 0.01$. Show more…

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The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or fewer errors in 100 pages?

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Key Concepts

Poisson Distribution

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, provided these events occur with a known constant mean rate and independently of the time since the last event.

Scaling of the Rate Parameter

When dealing with multiple independent intervals (such as pages in a textbook), the overall mean rate is scaled by the number of intervals. For example, if the average error rate is given per page, then for 100 pages the mean (lambda) becomes the rate per page multiplied by 100.

Cumulative Distribution Function (CDF) for Poisson Distribution

The CDF of a Poisson-distributed variable gives the probability that the number of events is less than or equal to a certain value. It is calculated by summing the individual probabilities from zero up to the target number of events.

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