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 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.
- 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 “”.
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
The results are not ok.