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Homework Help: Solving Normal Curve Questions using z-scores

  1. Nov 3, 2007 #1
    ok. mean ([tex]\mu\[/tex]) and standard deviation ([tex]\sigma\[/tex]) are unknown.
    20% of people scored less than 45
    and the top 15% scored greater than 87

    thus:
    P(x [tex]\leq\[/tex] 45) = .2
    P(x > 87) = 0.15, which needs to be converted to P(x [tex]\leq\[/tex] 87 ) = 0.85

    now using z scores ( z - [tex]\mu\[/tex]) / [tex]\sigma\[/tex]
    for part one:
    (45 - [tex]\mu\[/tex]) / [tex]\sigma\[/tex] = inverse normal (0.2)
    = -0.8416....
    rearranging to make 45 the subject:
    -0.8416[tex]\sigma\[/tex] + [tex]\mu\[/tex] = 45

    and for part 2:
    (87 - [tex]\mu\[/tex]) / [tex]\sigma\[/tex] = inverse normal (0.85)
    = 1.03643....
    rearranging to make 87 the subject:
    1.03643[tex]\sigma\[/tex] + [tex]\mu\[/tex] = 87

    this leaves to simulataneous equations:
    -0.8416[tex]\sigma\[/tex] + [tex]\mu\[/tex] = 45
    1.03643[tex]\sigma\[/tex] + [tex]\mu\[/tex] = 87

    which can be solved to give:
    [tex]\mu\[/tex] = 63.8
    [tex]\sigma\[/tex] = 22.4

    am i correct?
     
    Last edited: Nov 3, 2007
  2. jcsd
  3. Nov 4, 2007 #2

    EnumaElish

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