Question

Fill in the blanks. Suppose the probability at a light bulb factory of a bulb being defective is 0.11. If a shipment of 133 bulbs is sent out, the number of defective bulbs in the shipment should be around __________, give or take __________. Assume each bulb is independent.

Answer 1

The number of defective bulbs in the shipment should be around 15, give or take 4.

Explanation:

For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

The expected value of the binomial distribution is:

`E(X) = np`

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

Suppose the probability at a light bulb factory of a bulb being defective is 0.11

This means that
`p = 0.11`

Shipment of 133 bulbs:

This means that
`n = 133`

Mean and standard deviation:

`E(X) = np = 133*0.11 = 14.63`

`√(V(X)) = √(np(1-p)) = √(133*0.11*0.89) = 3.61`

Rounding to the nearest integers:

The number of defective bulbs in the shipment should be around 15, give or take 4.