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Math Help - probabilities

  1. #1
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    probabilities

    Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?
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  2. #2
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    Hello.

    Quote Originally Posted by jax760 View Post
    Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?
    So you ask about two different probabilities. first: exact 35 orders; second: exact 50 orders

    the probability "exact 35 orders" is according to the binomial distribution

    \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}

    p(exact 50 orders) = \begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}

    Edit:
    OH yea, actually it is "between 35 and 50". I didn't read the word "between". That makes a big difference. Thanks to mr fantastic

    In that case you have to sum the probabilities like this

    \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}+\begin{pmatrix} 500 \\ 36 \end{pmatrix}0.08^{36} * 0.92^{500-36}+...+\begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}

    Sorry for the mistake.

    Regards
    Rapha
    Last edited by Rapha; February 6th 2009 at 08:50 PM.
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  3. #3
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    Quote Originally Posted by jax760 View Post
    Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?
    Quote Originally Posted by Rapha View Post
    Hello.



    So you ask about two different probabilities. first: exact 35 orders; second: exact 50 orders

    the probability "exact 35 orders" is according to the binomial distribution

    \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}

    p(exact 50 orders) = \begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}

    Regards
    Rapha
    Actually the cumulative probability \Pr(35 \leq X \leq 50) is required where X ~ Binomial(n = 500, p = 0.08).
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