Chapter 14.4, Problem 18E

To determine

To Find: The number of month to which the guarantee should the guarantee to be limited.

Answer to Problem 18E

The manufacture must limit to 72.5 months guarantee.

Explanation of Solution

Given:

The mean length is 61 months and the standard deviation is 5 months.

The manufacturer do not want to replace any more than 2% of the CD players.

Calculation:

The objective to obtain the limit above which the 2% level of confidence is obtained.

The range of the interval about the mean has $x\%$ level of confidence have the probability $P=\left(100-x\right)\%$ for the sample of $P=\left(100-x\right)\%$ .

The range of the interval is obtained by the formula,

  $\left[\overline{X}-t{\sigma }_{\overline{X}},\overline{X}+t{\sigma }_{\overline{X}}\right]$

Here, the value of $t$ is the number of standard deviation.

Then, the number of months to which manufacturer must limit the guarantee is,

  $\begin{array}{c}\overline{X}+ts=61+2.3\left(5\right)\\ =61\pm 11.5\\ =49.5,72.5\end{array}$

Thus, the manufacture must limit to 72.5 months guarantee.