Question

soraya scored 69 in the class with the mean 78.7 and the standard deviation 5.1, but trashia scored 40 in the class with the mean 52.6 and the standard deviation 7. who scored relatively better? (round the answers to 2 decimal places)
sorayas z - score is
and trashias z - score is. since
sorayas z - score is select an answer trashias z - score, we conclude that
select an answer
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Explanation:

Step1: Calculate Soraya's z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For Soraya, \(x = 69\), \(\mu=78.7\), \(\sigma = 5.1\)

$$z_{Soraya}=\frac{69 - 78.7}{5.1}=\frac{-9.7}{5.1}\approx - 1.90$$

Step2: Calculate Trashia's z - score

For Trashia, \(x = 40\), \(\mu = 52.6\), \(\sigma=7\)

$$z_{Trashia}=\frac{40 - 52.6}{7}=\frac{-12.6}{7}=-1.80$$

Step3: Compare the z - scores

Since \(-1.80>-1.90\) (because when comparing two negative numbers, the one with a larger magnitude is smaller. For example, if \(a=-1.8\) and \(b = - 1.9\), \(a - b=-1.8+1.9 = 0.1>0\)), Trashia's z - score is greater than Soraya's z - score.

Answer:

Soraya's z - score is \(-1.90\) and Trashia's z - score is \(-1.80\). Since Soraya's z - score \( <\) Trashia's z - score, we conclude that Trashia scored relatively better.