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 he should use is

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

Hint:

Poisson is ideal for number of defects/rare events in a large sample when \(n\) is large and \(p\) is small.

Answer 1

The Correct Option is B

Step 1: Identify experiment type.
We check number of defective pins in a box of 100.
Each pin can be defective or not defective.
Step 2: Conditions for Poisson approximation.
Poisson is used when:
- number of trials \(n\) is large
- probability \(p\) is small
- expected value \(np\) is moderate
Here:
\[ n=100,\quad p=0.05 \Rightarrow np=5 \]
Step 3: Conclusion.
Since \(n\) is large and we deal with defect counts, Poisson distribution is suitable for approximating defective items.
Final Answer:
\[ \boxed{\text{Poisson distribution}} \]