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Poisson Approximation to Binomial Distribution An

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

Solution for problem 17BB 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 17BB

Problem 17BB

Poisson Approximation to Binomial Distribution An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6.

a. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times? Why or why not?

b. If the Poisson distribution is used, is the result OK? Why or why not?

Step-by-Step Solution:

Answer :

Step 1 :

Given, An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6.

  1. Where n = 12 and p = ⅙

         With n = 12 and p = 0.166, the condition n100is not satisfied. So we cannot use poisson distribution as an approximation to the binomial.

   b) Consider a random variable “x” follows poisson distribution with sample size “n” and parameter “”.

i,e.X P()

Probability mass function of poisson distribution is given by

P(x) = , x = 0,1,2,...,n.

       Where,  = np = 12(⅙) = 2

P(3)  =   = 0.180

Therefore the binomial distribution is

P(x) = (1 - p 

P(3)  =  (1 - 0.166   

         = 0.197

The results are not ok.

Step 2 of 1

Chapter 5.5, Problem 17BB is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Poisson Approximation to Binomial Distribution An