Question

The percentage of broken items in a factory is 0.006. Among 100 items chosen randomly, find out what is the probability that:

1) There is EXACTLY 1 broken item

2) There is AT LEAST 1 broken item

3) Recalculate the above probabilities using Poisson's approximation and comment of the results

Answer 1

Let X is a random variable shows the number of broken items. Here X has binomial distribution with following parameters

n=100, p=0.006

1)

The probability that there is EXACTLY 1 broken item is

2)

3)

Using Poisson approximation, X has Poisson distribution with following parameter

The probability that there is EXACTLY 1 broken item is

The probability that there is at least 1 broken item is