Question

A manufacturer makes 10 000 ball point pens per day and estimates that 150 will be defective.She decides that if a random sample of 20 pens contains more than one defective pen, then she will institute quality control measures. Find the probability that there are more than one defective.

Answer 1

Binomial distribution p=0.015, n=20

$P(>1)=1-P(\le1)$

$=1-\sum_{x=0}^1\binom{20}{x}0.015^x0.985^{20-x},x=0,1$

$=1-0.9643$

=0.0357

It is not likely that she will institute quality control measures.