The mean and standard deviation of the scores are 75 and 9.5 respectively.
The z-score is a means to find the probability of getting a particular score. This is calculated to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
To be a part of the top 2.5 percent, the probability is:
[tex]P=\frac{2.5}{100}=0.025[/tex]The z-score for this probability, that is, P
