The mean of normally distributed test scores is 81 and the standard deviation is 3. If there are 297 test scores in the data samoke, how many of them were in the 72 to 78 range?

Answer 1

First need to compute the probability that the score is between 72 and 78. That range is between 1 and 3 standard deviations away from the mean of 81 on the lower side. Per the empirical rule that range will occupy approximately 15.9 percent of the area under the normal curve so the probability the score is in that range is 0.159. You then multiply that number times 297 to determine the total number of students in that range.