Question

Apple uses cheap labor in factories in China to manufacture its cell phones. The probability that a phone is defective is 0.02. What is the probability that a sample of 500 iPhones will contain exactly 5 defective phones?

a.) What is the average number of defective phones?
(No decimals)

b.) The probability of getting 5 defective phones?
(To thousandths)

Answer 1

Let x be the random variable representing defective phone. Let n be the sample size. Let p be the probability that phone is defective.

Given: n=500, p= 0.02

From given information we know that x is random variable such that p is the probability of success and it is constant for each trial. Sample size n is fixed.

X follows Binomial distribution with parameters n=500 and p=0.02

a). The average number of defective phone

E(x) = n*p = 500 * 0.02 = 10

The average number of defective phones is 10.

b)Probability of getting 5 defective phones.

P(X=5) =
`(nCx) p^(x) (1-p)^(n-x)`

=
`(500C5) 0.02^(5) (1-0.02)^(500-5)`

= 0.037

The probability of getting exactly 5 defective is 0.037.