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Math Help - Probability

  1. #1
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    Probability

    A marketing research firm believes that approx. 25% of all persons mailed a sweepstakes offer will respond if a preliminary mailing of 5000 is conducted in a fixed region.

    a) What is the probability that 1000 or fewer will respond?

    a) What is the probability that 3000 or more will respond?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by r7iris View Post
    A marketing research firm believes that approx. 25% of all persons mailed a sweepstakes offer will respond if a preliminary mailing of 5000 is conducted in a fixed region.

    a) What is the probability that 1000 or fewer will respond?

    a) What is the probability that 3000 or more will respond?
    The number of responders has a binomial distribution B(0.25,5000). You are
    expected to use the normal approximation.

    The mean of the binomial is m=0.25 * 5000 = 1250, and standard deviation
    s=sqrt(5000*0.25*0.75) ~= 30.6.

    1000 or fewer corresponts to less than a z-score of (1000.5 - m)/s, which
    you look up in your normal table (the extra 0.5 is a continuity correction)

    3000 of more corresponds to more than a z-score of (2999.5-m)/s.

    RonL
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  3. #3
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    For the less than or equal to 1000 question, should it be (999.5-m)/s or (1000.5-m)/s?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by r7iris View Post
    For the less than or equal to 1000 question, should it be (999.5-m)/s or (1000.5-m)/s?
    No because every thing between 999.5 and 1000.5 rounds to 1000 which is in
    the range wanted.

    RonL
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