The probability that a person will die from a certain respiratory infection is 0.002 . Find the

Name: Problem 64, Chapter 5: Probability and Statistics for Engineers and Scientists
Uploaded: 2022-01-14T14:02:19-08:00
Duration: 2 min 2 s
Channel: Raymond Matshanda
Description: The probability that a person will die from a certain respiratory infection is 0.002 . Find the probability that fewer than 5 of the next 2000 so infected will die

step 1 All right, problem 64 says the probability that a person will die from a certain respiratory inf

The probability that a person will die from a certain...

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Key Concepts

Cumulative Distribution Function

This refers to the function that provides the probability that a random variable is less than or equal to a certain value. In the problem, calculating the probability that fewer than 5 individuals die involves summing the probabilities of 0, 1, 2, 3, and 4 deaths.

Binomial Distribution

This concept refers to a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials where each trial has the same probability of success. In the context of the problem, each person represents a trial with a small probability of death, and the total number of trials is 2000.

Poisson Approximation

When the probability of a success in a single trial is very small and the number of trials is very large, the binomial distribution can be approximated by the Poisson distribution. This method simplifies calculations, especially when the expected number of successes (np) is small, as is the case in the problem.

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