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Math Help - Problem with mean and standard deviation

  1. #1
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    Problem with mean and standard deviation

    A distributor of auto tires claims that 90% of its best brand of tires last more than 140, 000 Km. It has been shown that the lifetime of the tires of that brand has a normal distribution with mean 100, 000 Km and a standard deviation of 20, 000 Km. Is the vendor's claim accurate?

    We have done very basic problems like this in class but none this extensive.

    From this I know that μ = 100, 000 and σ = 20,000.

    I know I need to set up an inwquality with

    a ≤ [(x-100,000)/20,000] ≥ b

    but I don't know what a and b are to be and where the 140,000 and 90% fit in?

    Thank you
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  2. #2
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    You need to solve for x where

     P\left(Z<\frac{x-100000}{20000}\right)=.9

    If x = 140000 the claim is correct.
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