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Thread: rolling a die ...

  1. #1
    Dec 2005

    Question rolling a die ...

    Last edited by shirel; Aug 28th 2007 at 12:05 AM.
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  2. #2
    Grand Panjandrum
    Nov 2005
    Quote Originally Posted by shirel View Post

    A die is rolled 600 times. how many times does face 5 show up?
    Specify a reasonable range. Discuss why you prefer that one over other possible estimates.
    how certain is your estimate? For which range would you be absolutely certain?

    how would you answer?
    thanks for showing me your ideas, thoughts, explanations, calculations..

    See the answer to your other question about the distribution of the number
    of times a 5 will come up.

    Now 600 times is a large number of rolls so we may as well use the normal
    approximation to the binaomial distribution, in this case it will have mean:

    $\displaystyle m=Np = 600 \times (1/6) = 100$

    and standard deviation:

    \sqrt{Np(1-p)} = \sqrt{600(1/6)(5/6)} \approx 9.13

    So you would expect the number of 5's to be $\displaystyle 100 \pm k \times 9.13$, where
    the value of $\displaystyle k$ is chossen by you depending on what confidence you want
    that the actual number lies in the interval, often a value of $\displaystyle k=1.96 $ is used.

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