Answer to Z-Transformation Exercise #3

Z = (31 - 40) / 6 = -1.50
Drawing the figure shows that the Z-score is below the mean.

We look up 1.50 in the standard normal table. Since we are below the mean, we want to find the proportion beyond that Z-score.

That proportion is .0668.

Therefore, the percentile rank is (.0668)*100 = 7% (rounded to the nearest whole number).