Question

The manager of Toy World has decided to accept a shipment of electronic games if no more than 5 of a random sample of 21 is found to be defective. What is the probability he will accept the shipment if 14% of the games are defective?

Answer 1

The quantity of items in the shipment is not given. So the hypergeometric distribution cannot be applied as it normally should when sampling without replacement occurs and the shipment lot size is say two or three times the sample size.
Therefore the shipment lot size must be taken to be very much greater than the sample size and the probability of acceptance calculated using the binomial distribution.
The probability of there being 5 defective units (the maximum allowed for acceptance) in a sample of 21 units is found as follows:
\[\left(\begin{matrix}21 \\ 5\end{matrix}\right)0.14^{5}(1-0.14)^{21-5}\]
P(5 defectives)=0.09798
Probability of acceptance = 1 - 0.09798 = 0.90202 = 90% approximately