Question

A company manufactures fuses. From historical records it is known that 6% of all fuses manufactured at the company is defective. A random sample of 10 fuses is selected off the production line for inspection.

What is the probability (to 2 decimal places) that more than 8 fuses are manufactured without any defects?

Answer 1

This is a binomial distribution with n=10, p=1-0.06=0.94.

$P(X>8)=P(X=9)+P(X=10)=C_{10}^90.94^90.06^1+C_{10}^{10}0.94^{10}0.06^0=0.8824.$