Measuring Usability: Ask a Statistics Question

December 10, 2007 | asked by Anonymous :

Question : The grades on the midterm given in a large managerial stats class are normally distibuted with mean 75 and standard deviation 9. Instructors of this class wants to assign an A to top 10%, B to the next 10%, C to next 10%, D to next 10%, and an F to all scores below the 60th percentile. Find the lowest acceptable score within each established range. For example, the lowest acceptable score for an A is the score at the 90th percentile.

Answer : We need to use z-scores here to figure out the percentile grade cut-offs. We know the mean and standard deviation so we just need to figure out what data point we would use to get the z-scores that correspond to A:90, B:80, C:70, D:60, F:50 percent.

The easiest way I can think of doing this is setting up a simple equation and solve for the unknown scores from the z-scores for each percentile.
Find the z-scores for the percentiles 90, 80, 70 , 60 (we know 50 is 0). To do this you can use the percentile to z-score calculator.. We’re interested only on one-side of the area of the curve since a negative score is neither possible nor desirable (choose 1-sided) and get the z-scores for all cut-offs. For example you should get 1.28 for 90% (enter .90).
Setup the equation for each z-score. For example, for 90% the equation should be ( X – 75 ) / 9 = 1.28. Then isolate and solve for X (X-75 = 11.53396 so X = 86.53). Repeat this process for all scores.

Percentile	Z	Score	Grade
>=90	>=1.28	>=86.53	A
80	.841	82.57	B
70	.524	79.72	C
60	.253	77.28	D
<60	<.253	<77.28	F

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Question Tags

Tag Name	#	Vote
Percentile	1
Z-Score	1

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User Provided Answers & Comments :

December 11, 2007 | anonomous wrote:

Great! Thats what I got too, only I use 4 decimal values. Thanks for the help!

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