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Math Help - Probability problem

  1. #1
    Newbie Almondzqueen's Avatar
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    Red face Probability problem

    Here's a problem I'm stuck with:
    A survey for brand recognition is done and it is determined that 70% of consumers have heard of Mike's Mechanic Shop. A survey of 900 randomly selected cosumers is to be conducted. For such groups of 900, would it be unusual to get 527 consumers who recognized this shop? So I have to show all the statistics.....

    So I'm not clear whether I divide 527/900? Or do I multiply (900)*(.70)?
    And why would it be unusual? Do I have to draw a bell shaped curve as well (what would it look like)?
    I need this explained step by step.
    Thank you.
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  2. #2
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    pickslides's Avatar
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    So there was an initial survey that gave the figure of 70% and now there is another survey that will have 900 participants?

     \frac{527}{900} \approx 59\%

    you mentioned a bell shaped curve, are you given a standard deviation?
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  3. #3
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    Quote Originally Posted by Almondzqueen View Post
    Here's a problem I'm stuck with:
    A survey for brand recognition is done and it is determined that 70% of consumers have heard of Mike's Mechanic Shop. A survey of 900 randomly selected cosumers is to be conducted. For such groups of 900, would it be unusual to get 527 consumers who recognized this shop? So I have to show all the statistics.....

    So I'm not clear whether I divide 527/900? Or do I multiply (900)*(.70)?
    And why would it be unusual? Do I have to draw a bell shaped curve as well (what would it look like)?
    I need this explained step by step.
    Thank you.
    Assuming the figure of 70% is correct, the number of customers in the survey who have heard of the shop should have a Binomial distribution with p = 0.70 and n = 900. The mean of the distribution is np = 630. So I would interpret the question as asking what is the probability that 527 customers or fewer will recognize the shop. I.e., if X has a Binomial distribution with p = 0.70 and n = 900, what is the probability that X \leq 630? [Edit]Oops-- that should be 527.[/edit]

    You certainly wouldn't want to calculate this probability by hand, but you might have a calculator that will do it for you. Or you could use a Normal approximation to the Binomial-- that would be my choice.
    Last edited by awkward; October 3rd 2009 at 09:55 AM. Reason: fixed error
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  4. #4
    Newbie Almondzqueen's Avatar
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    Quote Originally Posted by pickslides View Post
    So there was an initial survey that gave the figure of 70% and now there is another survey that will have 900 participants?

     \frac{527}{900} \approx 59\%

    you mentioned a bell shaped curve, are you given a standard deviation?

    I actually remember her mentioning standard deviation but I can't find my notes that go with it! I do clearly remember her saying to use binomial distribution though. =/
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  5. #5
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    Please note that I wrote down a wrong number in my original post, which I went back and corrected.

    If you don't know the formula for the standard deviation of a binomial distribution, it is \sqrt{np(1-p)}.

    See
    Binomial distribution - Wikipedia, the free encyclopedia
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