Answer to Z-Transformation Exercise #5

Z = (230 - 310) / 150 = -.53
Drawing the figure shows that the Z-score is below the mean.

We look up .53 in the standard normal table. Since we are below the mean, we want to find the proportion beyond that Z-score.

That proportion is .2981.

Therefore, the percentile rank is (.2981)*100 = 30% (rounded to the nearest whole number).