SOLUTION: A certain brand of tyre manufactured by Run Wild Inc. has a lifetime that is normally distributed with a mean of 81,200 miles and a standard deviation of 4,300 miles. For how many

Question 1047222: A certain brand of tyre manufactured by Run Wild Inc. has a lifetime that is normally distributed with a mean of 81,200 miles and a standard deviation of 4,300 miles. For how many miles should they warranty their tyres if they want 95% of them to last longer than the warranty?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
For 95% to last longer, I need to have z>-1.645
z=(x-mean)/sd
-1.645=(x-81200)/4300 units in miles
Multiply both sides by 4300
-7073.5=x-81200
add 81200 to both sides
x=74126.5 miles
With a normal distribution with mean 81,200 and sd 4300, 95% of the values will be greater than 74,126.5 miles

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