Question

A light bulb factory produces 1,188 light bulbs every hour. Approximately 3.83% of the light bulbs are defective, and do not work. Using the binomial distribution, what is the standard deviation of the number of defective bulbs produced in an hour

Answer 1

The standard deviation of the number of defective bulbs produced in an hour is 6.615

Explanation:

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 standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

In this problem, we have that:

`p = 0.0383, n = 1188`

What is the standard deviation of the number of defective bulbs produced in an hour

`√(V(X)) = √(np(1-p)) = √(1188*0.0383*(1-0.0383)) = 6.615`

The standard deviation of the number of defective bulbs produced in an hour is 6.615