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Vera_Pavlovna [14]
3 years ago
6

President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests pe

rformed 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?
Mathematics
1 answer:
never [62]3 years ago
3 0

Answer:

2.28 %

Step-by-step 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)=\frac{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)=\frac{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.

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