Question

5.) Tom scored a 71 on his Physics exam and a 73 on his History exam. Tom was happy with his grade on the Physics test. He was told that the average grade on the test was a 60 with a standard deviation of 8. Tom was unhappy with his History grade because he was told that the average grade on that test was a 65 with a standard deviation of 6. Tom remarked that his relative standing in his Physics class was better than his relative standing in his History class. Is Tom correct?

Answer 1

We will compare the two given situations on the basis of Z-scores.

Z scores will tell us the relative comparison between two items.

Formula of Z score is,

T 11 Z=

where,

x is the observed value

$\mu$ is the mean

$\sigma$ is the standard deviation

Z is the z score

Now, we are given details about two subjects,

History

• x​​​​​​H = 73 marks
• 
  HH
  = 65 marks
• $\sigma_{H}$ = 6 marks

Physics

• x​​​​​​P= 71 marks
• $\mu_{P}$ = 60 marks
• $\sigma_{P}$ = 8 marks

Now we will calculate z scores for Physics and History named as Z​​​​​​P and Z​​​​​​H respectively.

$Z_{H} = \frac{x_{H}- \mu_{H}}{\sigma_{H}} = \frac{73-65}{6} = 1.34$

$Z_{P} = \frac{x_{P}- \mu_{P}}{\sigma_{P}} = \frac{71-60}{8} = 1.375$

Now, Z-score of Physics is greater than that of Z-score of History.

So, Tom was correct. His relative standing in Physics is better than History because Z-score of Physics is better than that of History.