Question

Large lots of spark plugs are being inspected for quality. A lot is considered acceptable if 5% or fewer of the spark plugs are defective. A random sample of 10 spark plugs is selected from a given lot. If the lot is acceptable, with only 1% defective spark plugs, what is the probability that none of the spark plugs in the sample are defective?

Answer 1

Let X denote the number of defective spark plugs in the sample. Then $X\sim Bin(n=10,p=0.01)$

$P(X=x)=\binom{10}{x}(0.01)^{x}(1-0.01)^{10-x},x=0,1,...,10$

Required probability = $P(X=0)=\binom{10}{0}(0.01)^{0}(1-0.01)^{10-0}=0.90438$