SOLUTION: Suppose that you are central General manager for tamanga tyres ltd. You want to set a minimum mileage guarantee on next XM70 tyre. Tests reveal the mean mileage is 47900 and with t

Question 1161020: Suppose that you are central General manager for tamanga tyres ltd. You want to set a minimum mileage guarantee on next XM70 tyre. Tests reveal the mean mileage is 47900 and with the standard deviation of 2050 miles and normal distribution. The manufacturer wants to set the minimum guaranteed mileage so that no more than 4 percent of tyre have to be replaced. What is the minimum guaranted mileage should the manufacturer announce

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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:
http://davidmlane.com/hyperstat/z_table.html
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.
$$$

when you use this online calculator, the area to the left of the z-score is what the calculator shows as below.

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