Question

A factory makes car batteries. The probability that a battery is defective is 1/14. If 400 batteries are tested, about how many are expected to be defective?

Answer 1

28.6, that is, about 29 are expected to be defective

Explanation:

For each battery, there are only two possible outcomes. Either it is defective, or it is not. The probability of a battery being defective is independent of other betteries. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

The probability that a battery is defective is 1/14.

This means that
`p = (1)/(14)`

400 batteries.

This means that
`n = 400`

How many are expected to be defective?

`E(X) = np = 400*(1)/(14) = 28.6`

28.6, that is, about 29 are expected to be defective