Question

President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated:

(1) an average life of 75 months,
(2) a standard deviation of 5 months,
(3) a bell shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use?

Answer 1

2.28 %

Explanation:

It is stated that battery life distribution is normal. First we need to find out where 65 hour battery life in this distribution falls by finding its z-score. We can use the following formula

z(x)=
`(X-M)/(s)` where

• X the point we are looking to find its z-score, which is 65
• M is the mean of the sample, which is 75
• s is the standard deviation of the sample, which is 5

Replacing these numbers in the formula, z-score of the 65 hour battery life :

z(x)=
`(65-75)/(5)`=-2

All the batteries fail within the first 65 months if their z-score is smaller than -2. Or we can state this also as: P(z≤-2) which is 0.0228

Thus 2.28 % of the batteries will fail within the first 65 months of use.