Download 21 - QC Economics

Geordan Hull
Queens College
Economics 249
CHAPTER 6, PAGE 261, QUESTION 21
Given:
 Mean (mew) = 100
 S.D. = 15
 I.Q. score is in the top 2%
Things to consider:
 Z = (X – Mew) / Sigma
 Z values measure how many standard deviations your x values are away from the mean
 Z tables provide you with the probability of a certain z value (standard deviation) occurring
 Z table graphs include the particular z value and all the values to the left
 If you know the probability, you need to find the corresponding z value
 1.0 = 100%, 0.98 = 98%, and 0.02 = 2%
Solution:
 100% - 2% = 98%
 The likelihood of scoring in the top 2% is the same as 1 minus the likelihood of scoring in
the bottom 98%
 1 – Probability (x less than or equal to bottom 98) = Probability (x greater than or equal to
top 2%)
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Probability of 98%  (2.05 + 2.06) / 2 = 2.055
P(X less than or equal to 2.055 ) = 98%
2.055 = (X – 100) / 15
2.055 * 15 = (X – 100)
(2.055 * 15) +100 = X
X = 130.825
Therefore, the cut-off I.Q. score to be in the top 2% is approximately 131 points.