Question

A manufacturer of cotter pins knows that $5\%$ of his product is defective.

He sells pins in boxes of $100$ and guarantees that not more than one pin will be defective in a box.

In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ, is

• A. Binomial
• B. Poisson
• C. Normal
• D. Exponential

Answer 1

The correct option is B

Poisson

Finding the probability distribution:

Here,$n=100$, in which the number of trials is very large

The probability given here is

$\begin{array}{rcl}5\%& =& \frac{5}{100}\\ & =& \frac{1}{20}\end{array}$,

which is very small.

A Poisson distribution is a tool that helps to predict the probability of certain events happening when you know how often the event has occurred.

It gives us the probability of a given number of events happening in a fixed interval of time.

Since the probability is very small and the number of trials is large, we use Poisson Distribution

Therefore, to find the probability value, one has to employ the Poisson distribution.

Hence, the correct answer is option (B).