Question

The grade point average (GPA) of the students at Lakeview High School is normally distributed with a mean of 3.1 and a standard deviation of 0.3. If there are 1800 students enrolled at the school, approximately how many have a GPA between 2.5 and 3.7?

Answer 1

Approximately 1718 have a score within that range.

We calculate the z-score for each end of this spectrum:

z = (X-μ)/σ = (2.5-3.1)/0.3 = -0.6/0.3 = -2

Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this z-score is 0.0228.

For the upper end:
z = (3.7-3.1)/0.3 = 0.6/0.3 = 2

Using a z-table, we see that the area to the left of, less than, this z-score is 0.9772.

The probability between these is given by subtracting these:
0.9772 - 0.0228 = 0.9544.

This means the proportion of people that should fall between these is 0.9544:
0.9544*1800 = 1717.92 ≈ 1718