Question

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?

Answer 1

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:

`\begin{gathered} Standard\text{ Deviation of the sample mean =} \\ (\sigma)/(√(n)) \end{gathered}`
`=\text{ }(1595)/(√(231))`
`=\text{ 104. 94 hours}`

CONCLUSION:

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

`=\text{ 104. 94 hours}`