Using z-scores, it is found that Julie's total is better as she scored above the mean in both tests.
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In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations X is above or below the mean.
- For the first test, [tex]\mu = 65, \sigma = 10[/tex].
- For the second test, [tex]\mu = 80, \sigma = 5[/tex].
Derrick:
- On the first test, scored 80, thus, the z-score is:
[tex]Z = \frac{80 - 65}{10} = 1.5[/tex]
- On the second test, also 80, thus:
[tex]Z = \frac{80 - 80}{5} = 0[/tex]
Julie:
- On the first test, scored 70, thus, the z-score is:
[tex]Z = \frac{70 - 65}{10} = 0.5[/tex]
- On the second test, also 90, thus:
[tex]Z = \frac{90- 80}{5} = 2[/tex]
Julie had positive z-scores in both tests, so she scored better.
A similar problem is given at https://brainly.com/question/16645591
