Chapter 9, Problem 3SE

Exam Scores The distribution of the scores on a certain exam is $N\left(80,5\right)$ which means that the exam scores are Normally distributed with a mean of 80 and a standard deviation of 5.

a. Sketch or use technology to create the curve and label on the $x\text{-axis}$ the position of the mean, the mean plus or minus one standard deviation, the mean plus or minus two standard deviations, and the mean plus or minus three standard deviations.

b. Find the probability that a randomly selected score will be greater than 90. Shade the region under the Normal curve whose area corresponds to this probability.