The grades on the last math exam had a mean of 72%. assume the population of grades on math exams is known to be distributed normally, with a standard deviation of 5%. approximately what percent of students earn a score between 72% and 87%? explain each step.

The exam scores are distributed normally with mean 72 and standard deviation 5.
Recall the empirical (68 - 95 - 99.7) rule, which says that approximately 95% of a normal distribution lies within two standard deviations of the mean. Put another way,



Also recall that the normal distribution is symmetric about its mean. This means that



From this last equation, it follows that



That is, about 47.5% of the students scored between 72 and 87 on the exam.