Answer to Question #115699 in Statistics and Probability for Nyarko Richard

Question

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

P(defective) =p=0.03

q=1-p=1-0.03

n=20

Let x represent the number of defective chips.

Probability that at least 2 are defective

$P(x\geq 2)$

P(X=x) =${n\choose x} p^x q^{n-x}$

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

=0.1198