Statistics Help!!

Question

A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 20 items are readied for shipment, and a sample of 10 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped. 

Now, suppose that the manufacturing company develops a new scheme: an inspector takes one item at random, inspects it, and then replaces it in the box; next 8 inspectors do likewise. Finally, a tenth inspector goes through the same procedure. The box is not shipped if any of the ten inspectors find a defective. 

Q: What is the probability that a box containing only one defective will be sent back for screening? 

Use normal approximation for answering !!!!

Answer 1

You would not use a normal approximation, but you could possibly use a Poisson approximation.

For p = 1/20 and n = 10, lambda = .5

P(x >= 1) = 1 - exp(-λ) = 1 - exp(-.5) = 0.393469340287367

The exact answer would be 1- .95^10 = 0.401263060761621