the random variable x is normally distributed with a mean of 75 and a standard deviation of 15.0. For this distribution, what is the twenty-third percentile?

Answer 1

23% of the population is below x = 64, if that is what you mean.

See http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
for how I got that.

Answer 2

Z = (score-mean)/SD

If you do not have a computer available, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion to help you find the above Z score and then the specific score.