Chapter 12.5, Problem 23HP

To determine

To Calculate: The light bulbs that will last between 260 and 340 days.

Answer to Problem 23HP

The correct option is D.

Explanation of Solution

Given information:

The mean lifetime of bulbs in days = 300.

The standard deviation in days = 40.

The range of middle 68% of data in a normal distribution = $\mu -\sigma$ to $\mu +\sigma$ .

So, substitute 300 for and 40 for.

Therefore, the range of values in the middle 68% will be:

  $\begin{array}{l}=(\mu \pm \sigma )\hfill \\ =(300\pm 40)\hfill \\ =(260,340)\hfill \end{array}$

Now, find 68% of 10,000 light bulbs as below:

  $\frac{65}{100}\times 10,000=6800$