Chapter 11.5, Problem 27STP

To determine

To find: The correct option.

Answer to Problem 27STP

The correct option is D

Explanation of Solution

Given:

The lifetime of 10,000 light bulb is normally distributed and the mean lifetime is 300 days and the standard deviation is of 40 days.

The objective is to obtain the number of light bulb that will last between 260 and 340 days.

Calculation:

Consider the empirical rule that the 68% of the data fall within 1 of the mean to calculate the number of light bulbs that is between 260 and 340 days.

Consider that the middle 68% of the data is a normal distribution is the range from the $\mu -\sigma$ to $\mu +\sigma$ . Then, the substitute 300 and 40. Thus, the range of the values in the middle 68% that is,

  $\begin{array}{c}\mu +\sigma =\left(300-40,300+40\right)\\ =\left(260,340\right)\end{array}$

Then, the 68% of the 10000 light bulbs is,

  $\frac{68}{100}\left(10000\right)=6800$

Thus, the current option is D.