A corporation has 250 personal computers. The probability...

Name: Problem 59, Chapter 4: Statistics for Business and Economics: Global Edition
Uploaded: 2021-12-29T00:58:40-08:00
Duration: 1 min 25 s
Channel: Christopher Stanley
Description: A corporation has 250 personal computers. The probability that any 1 of them will require repair in a given week is 0.01 . Find the probability that fewer than 4 of the personal computers will require repair in a particular week. Use the Poisson approximation to the binomial distribution.

A corporation has 250 personal computers. The probability that any 1 of them will require repair in a given week is 0.01 . Find the probability that fewer than 4 of the personal computers will require repair in a particular week. Use the Poisson approximation to the binomial distribution.

Key Concepts

Binomial Distribution

A binomial distribution models the number of successes in a fixed number of independent trials, where each trial has only two outcomes (success or failure) with a constant probability of success. It is used in situations where the outcome of each trial is independent and the probabilities remain the same.

Poisson Distribution

A Poisson distribution is used to model the number of events occurring in a fixed period of time or space when these events happen with a known constant mean rate and independently of the time since the last event. It is particularly useful for rare events in a large number of trials.

Poisson Approximation to the Binomial Distribution

The Poisson approximation to the binomial distribution is an approach used when the number of trials is large and the probability of success is small. Under these conditions, the binomial distribution can be approximated by a Poisson distribution with a parameter lambda equal to the product of the number of trials and the probability of success.

Expected Value in Poisson Approximation

In the context of the Poisson distribution, the expected value, or lambda, represents the average number of events occurring in the given interval. It is calculated as the product of the total number of trials and the probability of a single event occurring, summarizing the central tendency of the distribution.

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