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Math Help - Tchebysheff's Theorem

  1. #1
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    Tchebysheff's Theorem

    Here's my question : The U.S Mint produces dimes with an average diameter of .5 inch and standard deviation .01. Using Tchebysheff's theorem, find a lower bound for the number of coins in a lot of 400 coins that are expected to have a diameter between .48 and .52.

    -I just really am lost on this problem, anyone able to help?
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  2. #2
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    Quote Originally Posted by mathlete2 View Post
    Here's my question : The U.S Mint produces dimes with an average diameter of .5 inch and standard deviation .01. Using Tchebysheff's theorem, find a lower bound for the number of coins in a lot of 400 coins that are expected to have a diameter between .48 and .52.

    -I just really am lost on this problem, anyone able to help?
    Tchebysheff's or Chebyshev's inequality is:

    P(|X-\mu|>k\sigma )\le \frac{1}{k^2}

    In the case of the dimes we are being asked for bound on:

    P(|X-\mu|\le 2\sigma )=1-P(|X-\mu|> 2\sigma) \ge 1-\frac{1}{4}

    RonL
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  3. #3
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    reply to your query

    the answer to ur question is '300'. application of tchebysheff's formula. Sigma+-2(standard deviation) is the range of 0.48 to 0.52 - so going by tchebyscheff's theorem atleast 3/4 of the values(coins minted) will lie within the range provided. 3/4 of 400 = 300.
    guess you may have solved it yourself by now i just came upon this theorem and thought i'd look it up when i came across this bit...interesting but i wonder how long i'd retain it. all the best dude.


    Quote Originally Posted by mathlete2 View Post
    Here's my question : The U.S Mint produces dimes with an average diameter of .5 inch and standard deviation .01. Using Tchebysheff's theorem, find a lower bound for the number of coins in a lot of 400 coins that are expected to have a diameter between .48 and .52.

    -I just really am lost on this problem, anyone able to help?
    Follow Math Help Forum on Facebook and Google+

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