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Math Help - Show that p= 0.05

  1. #1
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    Show that p= 0.05

    The variable X has a binomial distribution with n=20 and probability of success p, where p<0.1.
    (i) write down an expression, in terms of p, for P(X=2).

    (ii) show that p=0.05, correct to 2 decimal places if given that P(X>=1) [x is larger or equals to 1)=0.641541

    Im having problems with part (ii)


    This is my attempt at it: If its rubbish, just ignore it! x.x

    P(X>=1) = 0.641541
    P(X>=1) can be written as 1-P(X=0)
    Hence,
    1-P(X=0) =0.641541

    Given that n=20

    20C0 x p^0 x (1-p)^20 = 0.641541
    1 x (1-p)^20 = 0.641541
    p^20= 0.641541
    p= 0.9780483099


    Thank you really really much!
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  2. #2
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    Re: Show that p= 0.05

    Quote Originally Posted by pumbaa213 View Post
    The variable X has a binomial distribution with n=20 and probability of success p, where p<0.1.
    (i) write down an expression, in terms of p, for P(X=2).

    (ii) show that p=0.05, correct to 2 decimal places if given that P(X>=1) [x is larger or equals to 1)=0.641541

    Im having problems with part (ii)


    This is my attempt at it: If its rubbish, just ignore it! x.x

    P(X>=1) = 0.641541
    P(X>=1) can be written as 1-P(X=0)
    Hence,
    1-P(X=0) =0.641541

    Given that n=20

    20C0 x p^0 x (1-p)^20 = 0.641541
    1 x (1-p)^20 = 0.641541
    p^20=0.641541
    you were fine up until here.
    you want to solve

    (1-p)^{20}=0.641541
    Thanks from pumbaa213
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  3. #3
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    Re: Show that p= 0.05

    I can't seem to solve it. could you help me a little more? thank you so much!
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  4. #4
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    Re: Show that p= 0.05

    really?

    (1-p)^{20}=0.641541

    1-p=\sqrt[20]{0.641541}

    p=1-\sqrt[20]{0.641541}

    p=0.022
    Thanks from pumbaa213
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  5. #5
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    Re: Show that p= 0.05

    yep! i got 0.022 as well but aren't I supposed to show that p=0.05?
    But thanks so much for the help, i really appreciate it!
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  6. #6
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    Re: Show that p= 0.05

    Quote Originally Posted by pumbaa213 View Post
    yep! i got 0.022 as well but aren't I supposed to show that p=0.05?
    But thanks so much for the help, i really appreciate it!
    I see what the problem is.
    We should be solving

    (1-p)^{20}=(1-0.641541)=0.358459

    p=1-\sqrt[20]{0.358459}=0.05
    Thanks from pumbaa213
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  7. #7
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    Re: Show that p= 0.05

    thank you so so so much romsek!
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