Question

A company is interested in tracking defective capacitors. The process normally yields 5% defective product. A sample of 400 capacitors is selected.

Explain why we would use the binomial distribution in this case

Answer 1

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times. The binomial is a type of distribution that has two possible outcomes . For example, a coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: pass or fail.

The first variable in the binomial formula, n, stands for the number of times the experiment runs. The second variable, p, represents the probability of one specific outcome (success).

Binomial distributions must also meet the following three criteria:

1. The number of observations or trials is fixed.  
2. Each observation or trial is independent. In other words, none of your trials have an effect on the probability of the next trial.
3. The probability of success is exactly the same from one trial to another.

Here n=400

So number of observations are fixed.

If we treat defective item as success then

p=0.05

Getting one item defective is independent of getting another item defective.

Also probability of getting defective item is same for each trail.

Because of all these, we would use the binomial distribution in this case.