Poisson Approximation to Binomial Distribution An experiment consists of rolling a

Step 1 of 2

Given that,

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.

The Binomial distribution is approximated with Poisson distribution only if the sample size n is so large; that is, .

Concerning the problem,

A single die is rolled 12 times indicating the number of trials to be n = 12 (very less than 100) Moreover, the probability that the outcome is 6 is  .

So,

With  , the requirement of is not fulfilled. Thus, the Poisson distribution is not a good approximation to the binomial distribution.

Hence,

The Poisson distribution cannot be used to find the probability that the outcome of 6 occurs exactly 3 times.