Answer to Question #119422 in Statistics and Probability for Nk

Question

A17. Suppose that 3% of computer chips produced by a certain machine are defective. The chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective chips?

Answer 1

This is a binomial distribution case $P(X=x) ={n\choose x} p^x q^{n-x}$

The probability of obtaining defective chips is p=0.03, which implies that q=1-p=1-0.03=0.97

n=20

Probability that at least 2 chips are defective

$P(x\geq 2)$

$P(X \geq 2)=\sum_{x=2}^{20} 0.03^x 0.97^{20-x}$

=0.12