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

Answer:

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

Step-by-step 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:

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

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

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1188*0.0383*(1-0.0383)} = 6.615$

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