What percentage of the students had scores between 65 and 85?

Question

Suppose that your class took a test and the mean score was 75% and the standard deviation was 5%. If the test scores follow an approximately normal distribution, answer the following questions:

Answer 1

Find the area under the curve for 65 and subtract it from the area under the curve for 85.

The z score for 65 is (65-75)/5 = -2, so looking on the negative z table you get 0.0228

The z score for 85 is (85-75)/5 = 2, so looking on the positive z table you get 0.9772

Subtract 0.0228 from 0.9772 and you get the probability for selecting a score between 65 and 85: 0.9544