Example 14: Convert the scores to standard z-scores and state which student has

Question

Example 14: Convert the scores to standard z-scores and state which student has the best score. Answer questions a - e below and write Z scores to 2 decimal places. (a) Mary's grade is 75, class mean-68 and class standard deviation-8; z = (b) John's grade is 80, class mean-70 and class standard deviation = 14; (c) Matt's grade is 90, class mean-74 and class standard deviation = 10; z- (d) Sue's grade is 85, class mean = 62 and class standard deviation-12; z- (e) Which student has the best score?

Explanation / Answer

Z score = X - mean / standard deviation.

a)

Z = 75 - 68 / 8

= 0.88

b)

Z = 80 - 70 / 14

= 0.71

c)

Z = 90 - 74 / 10

= 1.6

d)

Z = 85 - 62 / 12

= 1.92

e)

Z score for Sue's grade is better than other students.

Therefore, Sue has the best score.

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