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Math Help - Binomial Probability

  1. #1
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    Joined
    Sep 2011
    Posts
    4

    Binomial Probability

    Hi, the following is a list of binomial cumulative distribution of the probability that out of 25 investors, the number of investors that would have exchange-traded funds in their portfolios.

    We were asked for the probability that at least 14 investors do not have exchange-traded funds in their portfolios from this table.

    Binomial
    n 25
    p 0.4800

    xi P(X<=xi)
    0 0.0000
    1 0.0000
    2 0.0000
    3 0.0002
    4 0.0009
    5 0.0037
    6 0.0124
    7 0.0342
    8 0.0795
    9 0.1585
    10 0.2751
    11 0.4220
    12 0.5801
    13 0.7260
    14 0.8415
    15 0.9197
    16 0.9648
    17 0.9868
    18 0.9959
    19 0.9989
    20 0.9998
    21 1.0000
    22 1.0000
    23 1.0000
    24 1.0000
    25 1.0000

    Here is what I did: since they ask for at least 14 do not, it means 11 or less do. So the answer is .422---the cumulative of 11 and less that do.

    But when I used the Binomial Cumulative Distribution function on my calculator Binomcdf (25, 0.52, 14), I get 0.725.

    Where did I do wrong?

    Thanks.
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  2. #2
    Newbie
    Joined
    Sep 2011
    Posts
    13

    Re: Binomial Probability

    Just to clarify:

    p = .48 is the probability that an investor has exchange-traded funds in their portfolio.

    Thus

    p =.52 is the probability that an investor does not have exchange-traded funds in their portfolio.

    Thus, if you want to find the probability that at most 11 people have exchange funds in their portfolio, you would use:

    binomcdf(25, 0.48, 11).

    The parameters are (trials, prob of success, max # of successes)

    Your answer would have worked if the last parameter meant "at least k successes". But it means -at most- k successes.
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