Score
Z Scores
Z-Scores
The graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardized test is normally distributed?
The cut off score is determined by identifying the z-score associated with that percentile and computing the raw for that z-score (Aron, Coups, & Aron, 2011).
Z=
Transposing for X
The cut off score is 629
The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be:
Longer than 80 minutes?
Less than 50 minutes?
Between 45 and 75 minutes?
The proportion of commutes would be determined by computing the z-score for the relevant times and examining the proportion of the curve that are beyond, below and between the computed z-scores (Levin, Fox, &, Forde 2010).
a) Longer than 80 minutes
Using formula Z=X- ? + ?
Z=80-60/15
=20/15
=1.33
P= Area of the curve beyond 1.33
=0.0918 or 9.18%
b) Less than 80 minutes
Using formula Z=X-? + ?
Z=50-60/15
=10/15
=-0.67
P= Area of the curve below -0.67
P=0.2514
%=25.14%
Between 45-75
Using the formula Z=X-? + ?
Z (45) =45-60/15
=-1
Z (75) = 75-60/15
=1
P between -1 and 1
= 0.3413 + 0.3413
=0.6826
% =68.26%
Question 3
Bob takes an online IQ test and finds that his IQ according to the test is 134. Assuming that the mean IQ is 100, the standard deviation is 15, and the distribution of IQ scores is normal, what proportion of the population would score higher than Bob? Lower than Bob?
Proportion higher than Bob would be the area of the curve beyond Bob's score, the proportion lower than Bob would be the area of the curve below Bob's score.
Using the formula Z=X-? + ?
Z =134-100/15
=34/15
=2.27
P Higher than Bob's Score = 0.0116
P Lower than Bob's Score =0.9984
References
Aron A., Coups E.J., & Aron, E.N. (2011). Statistics for the behavioral and social sciences: A brief course. New York NY: Prentice Hall.
Levin, J. Fox, J.A., &, Forde, D.R. (2010). Elementary Statistics in Social Research. Boston MA: Allyn & Bacon.
