Question

Which has a better relative position: a score of 75 on a statistics test with a
mean of 60 and a standard deviation of 10 or a score of 36 on an accounting
test with a mean of 30 and a variance of 16?Justify your answer.

Answer 1

Please send help

Answer 2

you can think about relative position in terms of z-score. a higher z-score means a better position relative to the other sets in the data.

\[z-score = \frac{ x-μ }{ σ }\]
where x is the value being examined, μ is the mean, and σ is the standard deviation

so in the first case: the x is the score (75), the mean μ is 60, and the standard deviation σ is 10. plug in and evaluate the z-score

repeat this process for the second test score, then compare the z-scores. **important** because they give you variance for the 2nd score, take the square root of the variance first to get the standard deviation.