Question

Suppose that the mean and standard deviation of the scores in a Statistics exam are 75 and 9.5 respectively. What minimum score should a student obtain to be a part of the top 2.5%? Round answers to 2 decimal places.

Answer 1

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:

$z=\frac{x-\mu}{\sigma}$

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:

$P=\frac{2.5}{100}=0.025$

The z-score for this probability, that is, P