probability question

Question

The results for a university entrance exam are normally distributed with µ=48 and σ=9. What is the probability that an exam chosen at random will have a score greater than 63, but less than 73? Use the “Areas Under the Normal Distribution Curve” table on the last page of this exam. (Assume data is continuous)      

Answer 1

First we calculate the z-scores.

Z-score = (x - μ)/σ

For a score of 63: z-score = (63 - 48)/9 = 1.67

For a score of 73: z-score = (73 - 48)/9 = 2.78

Then calculate the area to the left of the larger (2.78) from the table. My table shows 0.99728. If you need help reading the table, let me know.

Then calculate the area to the left of the smaller (1.67). My table shows 0.95254

Then subtract the two answers: 0.99728 - 0.95254 = 0.04474 = about 4.5%

A picture of what's happening is this:

You are first figuring out the area in red, then the area in blue, then subtracting the two to get the area in gray.