Math Statistics

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An investigational drug study is being conducted. The initial screening phase needs to include enough people so that the final (approved) group has at least 10 patients. The probability of a person being approved for the study is .80. what initial sample size is needed to make sure with a .939 probability that the study will have at least 10 patients?

i don't know how to go about working this problem. i know its a discrete random variable problem and i know that i somehow have to work backwards, but i have NO idea how to set it up or work it. any and all guidance would be appreciated. thank you!!!

i don't expect you to work it for me, but i do need some help.

  • Math Statistics -

    would this be a binomial-like should i consider it

    applicable for study
    not applicable for study

  • Math Statistics -

    Yes, the binomial distribution is a discrete random variable problem.

    Basically, if you screen N people, each having a success rate of 0.8. You would like to calculate the minimum candidates to have a minimum of 10 success with a probability of 0.939.

    It is a very similar process to flipping coins, except the probability of success is 0.8 instead of 0.5.

    The probability can be obtained by tabulation, but the a formula exists to calculate the probability of success of n times out of N candidates, with a probability of success of p.

    P(n,N,p)=NCn*pN*(1-p)(N-n)

    Let say, since the proability of success is 0.8, and 10 people are required, a good starting point is to screen 10/0.8=13 candidates.

    So N=13, p=0.8,
    P(10,13,0.8) = 0.246
    P(11,13,0.8) = 0.268
    P(12,13,0.8) = 0.179
    P(13,13,0.8) = 0.055
    Probability of retaining 10 or more candidates
    = 0.246+0.268+0.179+0.055
    = 0.747 < 0.939 required.

    So you could screen 14 candidates and calculate the probability. Keep increasing the number of candidates until you get the probability of 0.939 or higher.
    Total =

  • Math Statistics -

    Oh yes, here's a link for more explanation:

    http://stattrek.com/Lesson2/Binomial.aspx

  • Math Statistics -

    Also, in case you are not familiar with the notation,
    nCr is the combination function defined as:

    nCr
    = n!/((n-r)!r!)
    =n(n-1)(n-2)...(n-r+1)/r!

    For example,
    13C10
    =13*12*11/(1*2*3)
    =286

  • Math Statistics -

    thank you so much! i think i got it!

  • Math Statistics -

    what was the answer you finally got

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