Which score has a higher relative position, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? a score of 688 a score of 92 both scores have the same relative position.

A score of 92 has a higher relative position than a score of 688.

Zscore formula :

Score A :

Score, x = 92

Mean, m = 71

Standard deviation, s = 15

Zscore = (92 - 71) / 15 = 1.4

Score B :

Score, x = 688

Mean, m = 493

Standard deviation, s = 150

Zscore = (688 - 493) / 150 = 1.3

Comparing the Zscore values, 1.4 > 1.3

Hence, Score of 92 has a higher relative position.

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solution:

a score of 92 has z score of

z=\frac{x-μ}{σ}=\frac{92-71}{5}=1.40

a score of 688 has z score of

z=\frac{x-μ}{σ}=\frac{688-493}{150}=1.30

a score of 92 is better because its z score is higher

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