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

Given:

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

Using the Z-score formula,

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ Z=(36-42.5)/(6.5) \\ Z=(-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;

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