A machine producing hair pins produces 1 defective out of 400 on an average. If 100 hairpins are packed in each box.
In above problem, suppose the manufacturer gives guarantee that there will be less than 3 defectives in a box of 100. What is the probability that a box selected at random will meet the guarantee.
We have a Bernoulli trial - exactly two possible outcomes, "success" (the hairpin is defective) and "failure" (the hairpin is non-defective) and the probability of success is the same every time the experiment is conducted (a hairpin is produced).
The probability of each result
For those situations in which is large and is very small, the Poisson distribution can be used to approximate the binomial distribution.
We have a Poisson distribution,
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