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Poisson Approximation to Binomial Assume that we plan to

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 4BSC Chapter 5.5

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 4BSC

Problem 4BSC

Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1 /1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101 wins, we get an extremely small positive number, so is it correct to conclude that the probability of 101 wins is possible, but highly unlikely?

Step-by-Step Solution:

Answer :

Step 1 :

Given,  

We have a sample size of n = 100 and for one bet there is a p = 1/1000 probability of winning.

With n = 100 and p = 0.001, the conditions n100 and np 10 (np = 100 0.001 = 0.1) are satisfied. So we can use poisson distribution as an approximation to the binomial.

For 101 wins, the poisson approximation gives small positive probability.

The probability of 101 wins is zero, since it is impossible to have 101 wins in 100 tries.

Step 2 of 1

Chapter 5.5, Problem 4BSC is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

The answer to “Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1 /1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101 wins, we get an extremely small positive number, so is it correct to conclude that the probability of 101 wins is possible, but highly unlikely?” is broken down into a number of easy to follow steps, and 83 words. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. The full step-by-step solution to problem: 4BSC from chapter: 5.5 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM. Since the solution to 4BSC from 5.5 chapter was answered, more than 381 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Probability, Poisson, binomial, Approximation, use. This expansive textbook survival guide covers 121 chapters, and 3629 solutions. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12.

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Poisson Approximation to Binomial Assume that we plan to