Answer to Question #195191 in Statistics and Probability for Rohit

Question

It has been found that 2 % of the tools produced by a certain machine are defective . What is the probability that in a shipment of 4 0 0 such tools , 3 % or more will be prove defective ?

Answer 1

While the Binomial is technically the right way to do this, for sufficiently large n and small p, the Poisson distribution offers an approximation that’s easier to compute.

So 2% of 400 = 8

So the question is, given an Poisson distribution of defectives with average =8,

probability we get 12 or more defective, or

1-cumulative probability of getting 11 or less defective

In excel use =1-poisson.dist(11, 8, TRUE)=11.2%