Question

7.The life of a Goldline auto battery is normally distributed with a mean of 42.5 months and a standard deviationof 6.5. The battery warranty is 36 months. What percentage of batteries will not meet the warranty and willhave to be replaced for free?Answer:

Answer 1

Solution:

Given:

$\begin{gathered} \mu=42.5months \\ \sigma=6.5 \\ x=36\text{months} \end{gathered}$

Using the Z-score formula,

$\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{36-42.5}{6.5} \\ Z=\frac{-6.5}{6.5} \\ Z=-1 \end{gathered}$

To calculate the percentage of batteries that will not meet the warranty, we first find the probability.

From the Z-scores calculator, the probability of batteries that will not meet the warranty and will have to be replaced for free is;

$P(x

The percentage of batteries that will not meet the warranty and will have to be replaced for free is;

[tex]0.15866\times100=15.866\text{ \%}$

Therefore, the percentage of batteries that will not meet the warranty and will have to be replaced for free is 15.87%