Question

On a particular production line,the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What are the mean and variance of the number of defective bulbs?

Answer 1

Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.

Explanation:

Consider the provided information,

Let X is the number of defective bulbs.

Ten light bulbs are randomly selected.

The likelihood that a light bulb is defective is 5%.

Therefore sample size is = n = 10

Probability of a defective bulb = p = 0.05.

Therefore, q = 1 - p = 1 - 0.05 = 0.95

Mean of binomial random variable:
`\mu=np`

Therefore,
`\mu=10(0.05)=0.5`

Variance of binomial random variable:
`\sigma^2=npq`

Therefore,
`\sigma^2=10(0.05)(0.95)=0.475`

Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.