Answer:
[tex]P = 84\%[/tex]
Step-by-step explanation:
The average is:
[tex]\mu = 40,000\ miles[/tex]
The standard deviation is:
[tex]\sigma = 1,000\ miles[/tex]
We want the probability that a tire lasts more than 39,000 miles.
This is:
[tex]P (X>39,000)[/tex]
Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.
[tex]P (X> 39,000)\\\\P (X-\mu> 39,000-40,000)\\\\P (\frac{X-\mu}{\sigma}> \frac{39,000 -40,000}{1,000})\\\\P (Z> -1)[/tex]
This is:
[tex]P(Z> -1) = P(Z<1)[/tex] ---------- (For the symmetry of the standard normal distribution)
When you search for the normal standard table, you get the following value:
[tex]P(Z <1) = 0.8413\\\\P(Z> -1) = 0.8413[/tex]
