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Math Help - [SOLVED] Statistics - Binomial Distribution

  1. #1
    Member looi76's Avatar
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    Question [SOLVED] Statistics - Binomial Distribution

    Question:
    Given that D~B(12,0.7), calculate the smallest value of d such that P(D>d)<0.90

    Answer:
    n = 12, p = 0.7, q = 1 - 0.7 = 0.3, d=?
    I can't find the value of d! please help...
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  2. #2
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    I may be guilty of promoting myself here....but it's not for profit so I think it's OK.

    If you look in the MHF software forum you will find a little program I wrote. I think it would be useful to you.

    You can get the answer to your problem using the program but that's not really the point.

    If you play around with it a little you might understand the question better.

    As for answering the question properly...

    Do you know how to calculate P(D=0) or P(D=1) for example?
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  3. #3
    Member looi76's Avatar
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    Yes, I know how to calculate P(D=0)
    P(D=0) = 12C0 * 0.7^0 * 0.3^(12-0)
    = 1 * 1 * 0.000000531
    = 0.000000531
    I don't know how to get the value of d!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by looi76 View Post
    Question:
    Given that D~B(12,0.7), calculate the smallest value of d such that P(D>d)<0.90

    Answer:
    n = 12, p = 0.7, q = 1 - 0.7 = 0.3, d=?
    I can't find the value of d! please help...
    It wants you to find the samllest d such that:

    P(D>d)<0.90

    where:

    P(D>d)= \sum_{r=d+1}^{12} b(r;12,0.7) <0.9,\ d an integer \le 12

    where b(r;12,0.7) is the probability of exactly r successes in 12 Bernoulli trials with a single trial probability of success of 0.7

    Now work backwards from 12 adding probabilities untill the total is greater than 0.9, and that last term is your d

    RonL
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