Answer:
a) The probability of falling in the warranty period is 11.6%.
b) The warranty period need to be 19771 km to ensure that no more than 5 per cent of tires fail in the warranty period.
Step-by-step explanation:
a) To fall within the warranty period, the tire has to fail before the 20,000 km.
To calculate the probability, we first calculate the z-value:
[tex]z=\frac{X-\mu}{\sigma}=\frac{20000-20613}{512}= \frac{-613}{512}= -1.197[/tex]
Then, the probability of falling in the warranty period is:
[tex]P(X<20,000)=P(z<-1.197)=0.116[/tex]
b) To calculate this we have to go on from a P(z<z₁)=0.05. This happens for z=-1.645.
This corresponds to a value X of:
[tex]X=\mu+z*\sigma=20613+(-1.645)*512=20613-842=19771[/tex]
The warranty period need to be 19771 km to ensure that no more than 5 per cent of tires fail in the warranty period.
