Question 1189495
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Which of the following exam scores is better relative to other students enrolled in the course? 
(a) A psychology exam grade of 85; the mean grade for the psychology exam is 92 with a standard deviation of 3.5;
(b) An economics exam grade of 67; the mean grade for the economics exam is 79 with a standard deviation of 8;
(c) A chemistry exam grade of 62; the mean grade for the chemistry exam is 62 with a standard deviation of 5.
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For each exam/grade you should calculate its z-score; then compare three z-score to determine which one is higher.


Use the formula for z-score


    Z = {{{(x - mu)/sigma}}}


where


Z	=	standard score
x	=	observed value
mu	=	mean of the sample
sigma	=	standard deviation of the sample


Use this formula separately for each case.


(a)  {{{Z[a]}}} = {{{(85-92)/3.5}}} = -2;


(b)  {{{Z[b]}}} = {{{(67-79)/8}}} = -1.5;


(c)  {{{Z[b]}}} = {{{(62-62)/5}}} =  0.0.


So, the score {{{Z[c]}}} is highest.  It means that that the exam score is better (is the best) for this exam (c).    


The three Z-scores are in this order  {{{Z[a]}}} < {{{Z[b]}}} < {{{Z[c]}}}.
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Solved.