Chapter 11.5, Problem 22HP

To determine

To find: The number of portable media players if sample is normally distributed.

Answer to Problem 22HP

The numbers of portable media players are 9.

Explanation of Solution

Given:

The average battery life is $8.2$ hours.

The standard deviation is $0.7$ hours.

There are eight players which have a battery life greater than $9.3$ hours.

Calculation:

Use the empirical rule that $95\%$ of the data fall within 2 of the mean to calculate the number of media players that will last between $6.8$ and $9.8$ hours.

As the middle $95\%$ data in a normal distribution is the range from $\mu -2\sigma$ to $\mu +2\sigma$ .

Find the range as follows.

  $\begin{array}{c}\mu \pm 2\sigma =\left(8.2\pm 2\left(0.7\right)\right)\\ =\left(6.8,9.6\right)\end{array}$

The average life of the battery that is $9.3$ will lie in the above calculated range. Hence, $95\%$ will be required percentage to calculate the number of media players.

Find the number of media players as follows.

  $\begin{array}{c}\frac{95}{100}\times n=8\\ n=8.4\\ n\approx 9\end{array}$

Therefore, the numbers of portable media players are 9.