Fluorescent light bulbs have lifetimes that follow a normal distribution, with an average life of 1,276 days and a standard deviation of 1,595 hours. In the production process, the manufacturer draws random samples of 231 lightbulbs and determine the mean lifetime of a sample. What is the standard deviation, in hours, of this sample mean?

Respuesta :

SOLUTION:

Step 1:

In this question, we are given the following:

Fluorescent light bulbs have lifetimes that follow a normal distribution, with an average life of 1,276 days and a standard deviation of 1,595 hours. In the production process, the manufacturer draws random samples of 231 lightbulbs and determines a sample's mean lifetime. What is the standard deviation, in hours, of this sample mean?

Step 2:

The details of the solution are as follows:

[tex]\begin{gathered} Standard\text{ Deviation of the sample mean =} \\ \frac{\sigma}{\sqrt{n}} \end{gathered}[/tex][tex]=\text{ }\frac{1595}{\sqrt{231}}[/tex][tex]=\text{ 104. 94 hours}[/tex]

CONCLUSION:

The standard deviation, in hours, of the sample mean =

[tex]=\text{ 104. 94 hours}[/tex]