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

Answer:

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

Step-by-step 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:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

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:

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

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{133*0.11*0.89} = 3.61$

Rounding to the nearest integers:

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