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Math Help - standard normal2

  1. #1
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    standard normal2

    An economics test is taken by a large group of students. The test scores are normally sidtrbuted with mean 70, and the probability that a randomly chones studnet receives a score less than 85 is 0. 9332.
    Four students are chosen at random. What is the probability that at least one of them scores more than 80 points on this test.

    How do you do with 4 people? Thanks so much.
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  2. #2
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    You will need to set up the normal distribution first and work out the chances that just 1 person scores more than 80 points.

    Once you have gotten this, the probability that at least 1 out of 4 gets above 80, is just 1 - P(they all get less than 80).

    If this doesn't help I will explain more.
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  3. #3
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    Quote Originally Posted by TheBrain View Post
    - P(they all get less than 80).
    .
    How do I get it? Thank you
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  4. #4
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    Quote Originally Posted by 0123 View Post
    An economics test is taken by a large group of students. The test scores are normally sidtrbuted with mean 70, and the probability that a randomly chones studnet receives a score less than 85 is 0. 9332.
    This bit allows you to determin the standard deviation. 0.9332 is the
    probability of observing a z of less than 1.5 from a standard normally
    distributed random variable. So the z score corresponding to a mark
    of 85 is:

    z = \frac{85-70}{\sigma} = 1.5

    so:

    \sigma=10

    Four students are chosen at random. What is the probability that at least one of them scores more than 80 points on this test.

    How do you do with 4 people? Thanks so much.
    The probability p that at least 1 score more than 80 is 1 minus the probability
    that all score less than 80. So if Q(80) is the probability that one score less
    than 80, then:

     <br />
p = 1-[Q(80)]^4<br />

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    This bit allows you to determin the standard deviation. 0.9332 is the
    probability of observing a z of less than 1.5 from a standard normally
    distributed random variable. So the z score corresponding to a mark
    of 85 is:

    z = \frac{85-70}{\sigma} = 1.5

    so:

    \sigma=10



    The probability p that at least 1 score more than 80 is 1 minus the probability
    that all score less than 80. So if Q(80) is the probability that one score less
    than 80, then:

     <br />
p = 1-[Q(80)]^4<br />

    RonL
    Uhm. Funny. Because there are quite a lot exercices like this and I did them differently getting the right result.
    I used binomial distribution with P= (X> 80). Is it wrong? How is that we both come up with the right result?
    Thanks a lot
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by 0123 View Post
    Uhm. Funny. Because there are quite a lot exercices like this and I did them differently getting the right result.
    I used binomial distribution with P= (X> 80). Is it wrong? How is that we both come up with the right result?
    Thanks a lot
    Because They are the same thing.

    RonL
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    Because They are the same thing.

    RonL
    oh.
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