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Math Help - Possible z-test?

  1. #1
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    Possible z-test?

    For the 2009-2010 academic year, 2300 students applied to W. University. The average SAT score for all students applying was 1300 with a standard deviation of 100. If you take a random sample of 400 students who applied to the university, what is the probability that more than 15% of the students in your sample had an SAT score above 1400?

    I can't figure out what to do. Any help, please?
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  2. #2
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    Re: Possible z-test?

    Hey DrKittenPaws.

    Hint: Try treating the problem as a binomial problem where the probability of success is the same as getting a SAT score about 1400.

    Then the probability of more than 15% will be P(Binomial Distribution Successes > 0.15*400).
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  3. #3
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    Re: Possible z-test?

    would u explain this detail chiro
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  4. #4
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    Re: Possible z-test?

    The idea is that you get the probability of a success which corresponds to getting 1400 or higher.

    If this probability is the same for all people and all people are independent, then the distribution is a Binomial distribution with n people and parameter p = probability of success = probability of getting 1400 or higher for one person.

    Then just the probability for n = 400, that P(Binomial > 14) using either a computer or by using a Normal approximation.
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  5. #5
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    Re: Possible z-test?

    well why the intial info that mean score is 1300 and sd is 100 was given ,15% of 400 is 60

    ie p(more 60 students score >1400)


    wat is the variable x stand for ,is it the score then then wat is mean and sd here mean score still will remain the same ,well to be frank i am cmpltly lost


    u said p(binomial >14) ?
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  6. #6
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    Re: Possible z-test?

    Yes, you need to use the normal distribution given to calculate a probability P(One student getting 1400 or more SAT) and then use that for your Binomial distribution.

    A binomial distribution represents a probability of getting x coin tosses given that you tossed n coins where P(X = x) is that probability.

    Since you want to find the probability of 14 or more getting more than 1400 you know that if each person has the same independent probability p of doing so then the probability of more than 14 is P(X > 14) where X has a binomial distribution with n = 400 and p = probability you calculated = P(One student getting more than 1400 on SAT).
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