Exercise 59 Page 969

We have been told that in an entry exam, scores are normally distributed with a mean of $140$ and a standard deviation of $20.$ We want to find the probability that a person who took the test scored between $120$ and $160.$ To do so we will find the percentage of the scores that is between $120$ and $160.$ First, let's find the differences between the given scores and the mean $140.$ As we can see, both of the scores are $20$ units away from the mean. Now, we will express this difference in terms of the standard deviation. To do so, let's divide the difference by the standard deviation, $20.$ Thus, $160$ is $1$ standard deviation above the mean and $120$ is $1$ standard deviation under the mean. To find the percentage, we will shade the total percent of scores that are between $1$ standard deviation above the mean and $1$ standard deviation under the mean. Notice that we have $34\%$ between $120$ and $140,$ and $34\%$ between $140$ and $160.$ Last, we will calculate the total percent of the score by adding those percentages. The probability that a person who took the test scored between $120$ and $160$ is $68\%,$ which corresponds to option C.