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Unformatted text preview: ide shows that this is indeed the case. 1 27. I think what this problem means for us to do is to compare the actual proportion of GPA values further than 1.5 times the standard deviation to the proportion corresponding to a perfect bell- shaped curve. The mean and standard deviation are 3.72 and 0.14. (I sent these in an email. To calculate them, I used the following SAS code. It would have been fine to use pencil and paper.) data prob27; input gpa @@; datalines; 3.46 3.72 3.95 3.55 3.62 3.80 3.86 3.71 3.56 3.49 3.96 3.90 3.70 3.61 3.72 3.65 3.48 3.87 3.82 3.91 3.69 3.67 3.72 3.66 3.79 3.75 3.93 3.74 ; run; proc means data=prob27 mean stddev; The proportion outside the interval 3.72- 1.5(0.14) and 3.72+1.5(0.14) is 0.18. From page 32 of the textbook, we see that the proportion outside of one standard deviation should be 1.00- 0.68, and that outside of two standard deviations, there should 1.00- 0.95. The proportion 0.18 fits nicely between the two. Those of you wh...
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## This document was uploaded on 03/02/2014 for the course STATS 4150 at Barnard College.

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