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)= 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)==-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.