Joelle has a test score of 75% on a test with a mean of 62%. To get into SAIT, she needs to be in the top 20% of those who took the test. Wh

Assuming the scores obey a normal distribution the following cumulative probability graph should help:

This is the cumulative probability for a normal distribution with mean 0 and standard deviation of 1.

Here we have z = (Joelie's test score - mean test score)/standard deviation

We can see from the graph that to get into the top 20% (ie reach a cumulative probability of 0.8) z must be at least 0.842.  So:

0.842 = (0.75 - 0.62)/stddev

$${\mathtt{stdev}} = {\frac{\left({\mathtt{0.75}}{\mathtt{\,-\,}}{\mathtt{0.62}}\right)}{{\mathtt{0.842}}}} \Rightarrow {\mathtt{stdev}} = {\mathtt{0.154\: \!394\: \!299\: \!287\: \!410\: \!9}}$$

So the standard deviation is 0.154 or 15.4%.

At least, I think this is what you are after!