The problem was. Suppose that we estimate a linear relationship between number of paragraphs in an essay and the number of words. Suppose that the mean number of paragraphs is 12 with a standard deviation of 2. Suppose that the mean number of words is 2480 with a standard deviation of 100. Finally, suppose that r is .8

Predict how many words will be in an essay with 10 paragraphs.

b = rSy/Sx = (.8)(100)/2 = 40

a = 2500 - b(12) = 2480 -40(12) = 2000

Then, we have Y = a + bX, so if X is 10, then Y = 2000 + 40(10) = 2400

Note that this makes some intuitive sense. If the number of paragraphs is one standard deviation below the mean and the correlation is .8, then you would expect the number of words to be .8 standard deviations below the mean.