Question

4% of the lightbulbs produced at Shady Stan's lightbulb factory are defective. An inspector visits the factory and randomly grabs 200 lightbulbs. Find the mean and standard deviation.

Answer 1

Answer: Mean = 8 and standard deviation is 2.77

Step-by-step explanation:

The mean and standard deviation for a binomial distribution is given by :-

$\text{Mean}=np\\\\\text{Standard deviation}=\sqrt{np(1-p)}$, where n is the sample size and p is the probability of getting success.

Given : The proportion of the lightbulbs produced at Shady Stan's lightbulb factory are defective: p=0.04

Sample size : $n=200$

Then , the mean and standard deviation for a binomial distribution is given by :-

$\text{Mean}=200\times0.04=8\\\\\text{Standard deviation}=\sqrt{200(0.04)(0.96)}=2.7712812921approx2.77$