The number of typing errors made by a typist has a Poisson...

Name: Problem 127, Chapter 3: Mathematical Statistics with Applications
Uploaded: 2021-03-13T05:50:20-08:00
Duration: 2 min 16 s
Channel: Prashant Bana
Description: The number of typing errors made by a typist has a Poisson distribution with an average of four errors per page. If more than four errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped?

The number of typing errors made by a typist has a Poisson distribution with an average of four errors per page. If more than four errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped?

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Key Concepts

Poisson Distribution

The Poisson distribution is a discrete probability distribution used to model the number of events occurring within a fixed interval of time or space when these events happen with a constant mean rate and independently of the time since the last event. It is characterized by the parameter ?, which represents the average number of occurrences in the interval, and is commonly applied in scenarios where events occur randomly but at a predictable average rate.

Cumulative Distribution Function (CDF)

The cumulative distribution function for a discrete random variable is the sum of the probabilities for all outcomes up to a given value. It provides the probability that the variable takes a value less than or equal to a certain threshold, and is essential for determining the likelihood of an event falling within a specified range, especially in decision-making contexts.

Threshold-Based Decision Making in Quality Control

Threshold-based decision making involves setting a specific limit or cutoff value, such that if a measured quantity exceeds this threshold, a particular action is triggered—such as rejecting a product or reworking a page. This concept is important in applications where outcomes are monitored and managed to maintain quality or performance standards.

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