Raul received a score of 80 on a history test for which the class mean was 70 with standard deviation 10. He received a score of 75 on a biology test for which the class mean was 70 with standard deviation 2.5. On which test did he do better relative to the rest of the class?

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MrRoyal MrRoyal · Answer 1 · 2020-12-12T15:00:26+01:00

Answer:

Raul performed better in the biology test

Step-by-step explanation:

Given

History

[tex]Score = 80[/tex]

[tex]Mean = 70[/tex]

[tex]Standard\ Deviation = 10[/tex]

Biology

[tex]Score = 75[/tex]

[tex]Mean = 70[/tex]

[tex]Standard\ Deviation = 2.5[/tex]

Required

Where did he perform better relative to other students

To do this, we simply calculate the z score in both tests and make comparison.

z score is calculated as thus;

[tex]z = \frac{x - Mean}{SD}[/tex]

For history;

[tex]z = \frac{80 - 70}{10}[/tex]

[tex]z = \frac{10}{10}[/tex]

[tex]z = 1[/tex]

For biology;

[tex]z = \frac{75 - 70}{2.5}[/tex]

[tex]z = \frac{5}{2.5}[/tex]

[tex]z = 2[/tex]

Since the z score in the biology test is greater than that of the history test, then he performed better in the biology test