Question

A tyre manufacturer wants to set a minimum mileage guarantee on its new MX100 tyre. Tests reveal the mean mileage is 47,900 with a standard deviation of 2,050 miles and the distribution is a normal distribution. The manufacturer wants to set the minimum guaranteed mileage so that no more than 4% of the tyres will have to be replaced. What minimum guaranteed mileage should the manufacturer announce

Answer 1

51,487.5

Step-by-step explanation:

Calculation to determine the minimum guaranteed mileage should the manufacturer announce

Sinces no more than 4% of the tires will have to be replaced First step will be to determine the InvNorm(.96) using normal distribution table

InvNorm(100%-4%)

InvNorm(.96) = 1.75

Now let determine the minimum guaranteed mileage

Let x represent the Minimum guaranteed mileage

(2050*1.75)+47,900=x

x=3,587.5+47,900

x = 51,487.5

Therefore the minimum guaranteed mileage that the manufacturer should announce is 51,487