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Math Help - approximations of distributions

  1. #1
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    approximations of distributions

    In a multiple choice test have 200 questions, each with four possible answers, of which only one is correct. What is the probability that a student hit between 25 and 30 of 80 questions among 200 of which he knows nothing?
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  2. #2
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    You've identified what you need to do in the title (approximations of distributions). Where are you stuck?
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  3. #3
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    Quote Originally Posted by Apprentice123 View Post
    In a multiple choice test have 200 questions, each with four possible answers, of which only one is correct. What is the probability that a student hit between 25 and 30 of 80 questions among 200 of which he knows nothing?
    I'm confused by the wording. Is the number 200 irrelevant, and we're just considering the 80 questions for which the student guesses? Also, is "between 25 and 30" inclusive, as in {25,26,27,28,29,30} or exclusive as in {26,27,28,29}? I would assume inclusive, but it's nice if it's specified.
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  4. #4
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    My attempt

    p = 25% = 0,25
    P(25 < X < 30)
    P(X>25) = P(X > 25,5) by approximations of distributions
    Z1 = 1,42 -> 0,922196
    P(X<30) = P(X < 29,5) by approximations of distributions
    Z2 = 2,45 -> 0,992857

    Z2 - Z1 = 0,070661

    But the answer is 0,1196
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  5. #5
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    You have tried to do: P(25 < X < 30) = P(X<30) - P(X>25)

    it should be
    P(25 < X < 30) = P(X < 30) - P(X \leq 25)


    I assume the question actually wants P(25 \leq X \leq 30) which can be worked out as follows

    X \sim Bi(80,0.25)

    We will say this is approximated by
    Y \sim N(20,15)

    P(X \leq 30) \approx P(Y < 30.5) = \Phi(\frac{10.5}{\sqrt{15}}) = 0.9967
    P(X \leq 24) \approx P(Y < 24.5) = \Phi(\frac{4.5}{\sqrt{15}}) = 0.877361

    .9967-.877361 = .119286

    I assume the difference between me and the textbook is due to rounding.
    Last edited by SpringFan25; June 20th 2010 at 03:50 PM. Reason: replaced \sim with \approx
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  6. #6
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    You not used approximations of distributions ?
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  7. #7
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    indeed i did...

    Quote Originally Posted by Me
    We will say this is approximated by
    ...

    I have made minor changes to the original post in case it wasn't clear.
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  8. #8
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    Ohh yes. Thank you
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