Question 1161020
you are given he mean mileage on the tires is 47900 and the standard deviation is 2050 miles.
you want to set it up so that only 4% of the tires will not exceed a certain mileage.
you can use a z-score calculator to find out what the critical z-score it.
i used an online calculator found at:
<a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>
the critical z-score is -1.751 rounded to 3 decimal places.
to find the raw score, use the z-score formula of:
z = (x-m)/s
z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation
the formula becomes -1.751 = (x-47900)/2050
solve for x to get:
x = -1.751 * 2050 + 47900 = 44310.45
they can guarantee that the tires will last at least 44310.45 miles without 
 having to be replaced.
they will only have to pay to replace 4% of the tires when they fail to reach that mileage.
here are the results from using that calculator.
<img src = "http://theo.x10hosting.com/2020/061203.jpg" alt="$$$" >
when you use this online calculator, the area to the left of the z-score is what the calculator shows as below.