Question

What is the probability of finding three or fewer nonconforming items in a sample of 5 items from a lot that has 50 total items and ten of them are known to be nonconforming?

When using the Hypergeometric distribution to solve I get 0.9959 as opposed to the binomial distribution which gets me a result of 0.9933. Which would be the correct formula to use and why?

Answer 1

The basic difference between Hypergeometric and Binomial distribution is, the way the sampling is done.

• In case of Hypergeometric distribution the 5 items are selected from the lot of 50 items, using without replacement sampling technique.That means when we select one item we do not return that item back before selecting the next items.
• In case of Binomial distribution the 5 items are selected from the lot of 50 items, using with replacement sampling technique.That means everytime we select one item we return that item back before selecting the next items.

In this problem, we can use Hypergeometric disturbution because, if we use with replacement scheme and thus binomial distribution , there is a chance of getting a particular defective(or non defective ) item again and again in our sample.To avoid it, in case of practical situations we always prefer without replacement technique and hence Hypergeometric distribution.(However, if it is particularly mentioned in a problem to use binomial distribution or with replacement sampling is done, we have to use it.) So it solely depends on the way we have drawn the sampling units.

In the given problem nothing is mentioned regarding the way the sampling of 5 items is done from the lot of 50 items.So, we can go for Hypergeometric distribution that yields the required probability = 0.9959.