Question

Find the probability that at most 5 defective bolts will be found in a box of 200 bolts if it is known that 2 per cent of such bolts are expected to be defective .(you may take the distribution to be Poisson; e-4= 0.0183).

Answer 1

Here's one way to do this problem.

Poisson distribution (m = mean):
P(x) = e^(-m) m^x / x!
Note: mean = .02*200 = 4

Find P(0) through P(5). Add together for the probability.

Here's P(0):
P(0) = (e^ -4) (4^0) / (0!)
= (0.0183) (1) / (1)
= 0.0183


I hope this will help get you started.

Answer 2

0.031