If data are approximately normally distributed, the Empirical Rule provides percentages of data within 1, 2, and 3 standard deviations of the mean. Percentiles provide percentages below a specified value.

i) Find the percentiles for z = -3, -2, -1, 0, 1, 2, 3. Write these as percentages with two decimal places. Explain the percentile for z = -2 and z = 1.

Many colleges in the United States grant credits or advanced placement based on AP test scores. Most schools require a score of 3 or higher in order to obtain college credit for that particular course. In May 2016, the average score on the AP Music Theory exam was 2.99 with a standard deviation of 1.32.

ii) Assuming that AP Music Theory scores are approximately normally distributed, what score was at the 65th percentile. Would a student who scored at the 65th percentile be able to obtain college credit for Music Theory?