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Math Help - Tchebysheff's Theorem

  1. #1
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    Tchebysheff's Theorem

    A manufacturer of tires wants to advertise a mileage interval that excludes no more than 10% of the milage on tires he sells. All he knows is that, for a large number of tires tested, the mean mileage was 25000 miles, and the standard deviation was 4000 miles. What interval would you suggest?

    Just not sure on how to set this up, is it:
    P(|Y-25000|<k\sigma )\geq 0.1=1-\frac{1}{k^2}
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    Quote Originally Posted by Robb View Post
    A manufacturer of tires wants to advertise a mileage interval that excludes no more than 10% of the milage on tires he sells. All he knows is that, for a large number of tires tested, the mean mileage was 25000 miles, and the standard deviation was 4000 miles. What interval would you suggest?

    Just not sure on how to set this up, is it:
    P(|Y-25000|<k\sigma )\geq 0.1=1-\frac{1}{k^2}
    Do you have to use Tchebysheff's Theorem? If so, then it will be

    \Pr(|Y-25000| \geq k\sigma )\leq \frac{1}{k^2} = \frac{1}{10}.


    However, you can get much tighter bounds if you use the Central Limit Theorem: Y ~ Normal (\mu = 25000, \sigma = 4000) and find the value of y^* such that \Pr(|Y-25000| \geq y^*) = \frac{1}{10}.
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    Thanks!
    Yeah, the question is from the section on Tchebysheff's theorem
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