Question

A manufacturer of cotton pins knows that 5 percent of his product is

defective. If he sells cotter pins in boxes of 100, and guarantee that not more than 4

pins will be defective, what is the approximate probability that a box will, fail to

meet the guaranteed quality.

b) Which distribution is used in (a)also give the reason .

Answer 1

a) Using Bernulli formula:

$P(<=4) = 1 - P(0) - P(1) - P(2) - P(3) - P(4) = 1 - 0.95^{100} - 99×0.05×0.95^{99} - 97×49×0.05^2×0.95^{98} - 95×16×97×0.05^3×0.95^{97} - 93×94×95×4×0.05^4×0.95^{96} = 0.607.$

b) It is discrete binomial distribution, because it represents the probability for no more than 4 fails in 100 trials, given a fail probability of 0.05 for each trial.