Question

Some teachers grade on a "(bell) curve" based on the belief that classroom test scores are normally distributed. One way of doing this is to assign a "C" to all scores within 1 standard deviation of the mean. The teacher then assigns a "B" to all scores between 1 and 2 standard deviations above the mean and an "A" to all scores more than 2 standard deviations above the mean, and uses symmetry to define the regions for "D" and "F" on the left side of the normal curve. If 200 students take an exam, determine the number of students who receive a B. (Round to the nearest whole student.)

Answer 1

We need to find the proportion of students who will lie between 1 standard deviation and 2 standard deviation above the mean

For 2 SD above the mean, the z score = 2, and the probability = 0.9772

For 1 SD above the mean, the z score = 1, and the probability = 0.8413

Therefore the proportion of students between 1 and 2 standard deviations = 0.9772 - 0.8413 = 0.1359

Therefore the number of students who receive a B = 200 * 0.1359 = 27.18    27 students