The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

Answer 1

Her score is 2 standard deviations above the mean. Only 2.3% are higher.

Call it the 97th percentile

Answer 2

For a useful online tool for this type of question, see
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html