1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solving Normal Curve Questions using z-scores
  1. Normal Curve question (Replies: 6)

  2. Area between z scores? (Replies: 3)

Loading...