1. Limited time only! Sign up for a free 30min personal 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!

Finding z-scores

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Students who are in the top 16% and top 2.5% will graduate with special honours. Where should the limits be set in terms of z-scores?

    Mean (xbar) = 2.7
    Standard deviation (s) = 0.5


    2. Relevant equations

    z = x - xbar / s

    and

    -1 to 1 = 68% of all grades
    -2 to 2 = 95% of all grades
    -3 to 3 = 99.7% of all grades

    (don't know if that's ^ relevant)


    3. The attempt at a solution

    I tried multiplying 3 (the highest z score) by 0.84 (100 - 16) but that didn't seem to work. I know there's one thing I have to do before I use the z-score formula, but it's just not clicking.
     
  2. jcsd
  3. Nov 28, 2009 #2

    Mark44

    Staff: Mentor

    You need to look at a table of z-scores. You want the numbers z1 and z2 for which P(z < z1) = .84 and for which P(z < z2) = .975.

    After you get these numbers, you need to use the transformation formula to convert to x scores. The one you gave converts x-scores to z-scores. To get the transformation that goes from z-score to x-score, solve that formula for x.

    BTW, the formula you gave should be written as z = (x - mu)/sigma; i.e., you need parentheses, and it involves the population mean and population standard deviation, not the sample mean and standard deviation.
     
  4. Nov 29, 2009 #3
    I searched for a z-score table, but I don't know how to read it. On one axis they have z-scores and along the other axis are decimal values, but what are these values? How do I find 0.84 and 0.975 if they're not listed?
     
  5. Nov 30, 2009 #4

    Mark44

    Staff: Mentor

    One row will have 0.8. Look for the column with 4 in it. In the cell in the row with 0.8 and the column 4 is the probability that z < .84. The table I'm looking at has 0.7995 at that position.
     
  6. Nov 30, 2009 #5
    Alright, so 0.7995 corresponds to 0.84 and 0.83523 corresponds to 0.9775. But when I plug these values in and solve for x, I get virtually the same answers (3.1 and 3.11). How can that be?
     
  7. Nov 30, 2009 #6

    Mark44

    Staff: Mentor

    0.7995 is the probability that corresponds to a z-score of .84. Look in the body of the table for .9775 and find the z-score that corresponds to it?

    After you get the two z-scores, solve for x in the formula z = (x - mu)/sigma, and then use that new formula to calculate the two x-scores.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook