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Math Help - Normal Distribution

  1. #1
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    Normal Distribution

    Two questions any help would be great

    1. There is a normal distributed class average of 70 and a standard deviation of 10. So what would be the 20,60,80 percentiles???

    2.There is a normal distributed class with average(mean) of 71 and a standard deviation of 11.Find the quartiles(Q1,Q2,Q3)?
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  2. #2
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    Quote Originally Posted by someone21 View Post
    Two questions any help would be great

    1. There is a normal distributed class average of 70 and a standard deviation of 10. So what would be the 20,60,80 percentiles???

    2.There is a normal distributed class with average(mean) of 71 and a standard deviation of 11.Find the quartiles(Q1,Q2,Q3)?
    what have you tried?

    Find z such that:

    Pr(Z<=z) = 0.20
    Pr(Z<=z) = 0.60 = 0.50+0.10 = 1.00 - 0.40
    Pr(Z<=z) = 0.80 = 0.50+0.30 = 1.00 - 0.20
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    what have you tried?

    Find z such that:

    Pr(Z<=z) = 0.20
    Pr(Z<=z) = 0.60 = 0.50+0.10 = 1.00 - 0.40
    Pr(Z<=z) = 0.80 = 0.50+0.30 = 1.00 - 0.20
    SOrry but i just dont understand it how can be find the z score when we dont know what x value to plug in??

    anyways thanks for trying
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  4. #4
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    Quote Originally Posted by someone21 View Post
    SOrry but i just dont understand it how can be find the z score when we dont know what x value to plug in??

    anyways thanks for trying
    You have to use the concept of the inverse normal, which is what TKH was trying to push you towards.

    For example:

    \Pr (Z \leq z) = 0.20 \Rightarrow \Pr( Z > -z) = 0.20 \Rightarrow \Pr(Z < -z) = 0.8 \Rightarrow -z = 0.842

    using the ubiquitous four-figure math tables. Therefore z = -0.842.

    But you also know that Z = \frac{X - \mu}{\sigma}.

    Therefore 0.842 = \frac{x - 70}{10} \Rightarrow x = ....
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  5. #5
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    Part 1a)

    The 20th percentile in test scores is the test score which is surpassed by only 80% of the class. Likewise, the 60th percentile in test scores is the test score which is surpassed by only 40% of the class. Same deal with 80th percentile which is only surpassed by 20% of the class.

    Now, let's call x the 20th percentile test score. How do we find x? Use the z-score equation: z = \frac{x - \mu}{\sigma}

    We want the value of z that corresponds to .20. This value can be found using an online statistics applet (found in 30 seconds using google), or by reading your z-table (probably distributed countless number of times by your teacher and or in your text book). You will find that z = -0.84

    So, plug and chug to get x: -0.84 = \frac{x - 70}{10}

    Go from there and note that quartiles are the same question, just simply substitute for example, the first quartile with 25th percentile.
    Last edited by abender; May 16th 2008 at 03:22 AM. Reason: left pasted question in solution
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