Question
In: Statistics and Probability
A tire manufacturer believes that the life of its tires follow a normal distribution with a...
A tire manufacturer believes that the life of its tires follow a normal distribution with a mean of 46,000 miles and a standard deviation of 4,000 miles. What mileage can he guarantee each tire to last so that 99% of the tires last longer than the guaranteed lifetime?
Solutions
Expert Solution
Solution:
Given: A tire manufacturer believes that the life of its tires
follow a normal distribution with a mean of 
miles and a standard deviation of 
miles.
We have to find x = guaranteed lifetime so that:
P( X > x ) = 99%
P( X > x ) = 0.99
thus find z value such that:
P( Z > z ) = 0.99
that is find
P( Z < z) = 1 - P( Z > z )
P( Z < z) = 1 - 0.99
P( Z < z) = 0.01
look in z table for area = 0.0100 or its closest area and find z value.
Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03
thus z = -2.33
Now use following formula to find x value:
Thus 36,680 miles he can guarantee each tire to last so that 99% of the tires last longer than the guaranteed lifetime
orchestra answered 2 years agoRelated Solutions
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