4) On an exam with a mean of 75, you score an 80. Would you be in a better position if SD = 2 or SD = 10? Explain

For the distribution of the score in the exam, it is given that:

The mean, $\mu =75$

Individuals's raw score, $X$ (say) is $80$.

In order to compare the individual's performance on the exam, the raw score is standardized. The standardized score of an individual is given in terms of standard deviations of the distribution of the scores for the measured deviation between the raw score and the mean of the distribution of the scores. That is the standardized score, $z=\frac{X-\mu }{\sigma }$. Here $\sigma$ is the standard deviation.