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Math Help - binomial distribution, using cumulative distribution tables

  1. #1
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    binomial distribution, using cumulative distribution tables

    The random variable X~B( 50, 0.40). Find

    a) the largest value of k, such that  P(X\leq k)< 0.05
    B)the smallest number r, such that P(X>r) <0.01

    I have done part 'a', by simply looking at the tables, n=50, p=0.40 and looking for the value for X that gives a probability less than 0.05. Which is k=13.

    But I am stuck on part 'b', because it asks for x>r, and the tables only give values for  P(X\leq x )


    Can someone show me how to work this out?

    Thanks.
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    Quote Originally Posted by Tweety View Post
    The random variable X~B( 50, 0.40). Find

    a) the largest value of k, such that  P(X\leq k)< 0.05
    B)the smallest number r, such that P(X>r) <0.01

    I have done part 'a', by simply looking at the tables, n=50, p=0.40 and looking for the value for X that gives a probability less than 0.05. Which is k=13.

    But I am stuck on part 'b', because it asks for x>r, and the tables only give values for  P(X\leq x )


    Can someone show me how to work this out?

    Thanks.
    Note that P(X > r) = 1 - P(X \leq r).
    Last edited by awkward; March 21st 2010 at 12:10 PM. Reason: capitalization
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  3. #3
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    Quote Originally Posted by awkward View Post
    Note that P(X > r) = 1 - P(X \leq r).
    Thank you,

    But wouldn't I have to work out the value of 'r' before I do this?
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  4. #4
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    Quote Originally Posted by Tweety View Post
    Thank you,

    But wouldn't I have to work out the value of 'r' before I do this?
    No.

    P(X < r) < 0.01

    if and only if

    1 - P(X \leq r) < 0.01

    if and only if

    0.99 < P(X \leq r)
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