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IrinaVladis [17]
3 years ago
9

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?
Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:

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

Step-by-step 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 = \frac{1}{14}

400 batteries.

This means that n = 400

How many are expected to be defective?

E(X) = np = 400*\frac{1}{14} = 28.6

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

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