Content attribution
QUESTION $20 \cdot 1$ POINT
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 170 pages if the mean $(\mu)$ is 195 pages and the standard deviation $(\sigma)$ is 25 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
Provide your answer below:

Step 1 ：Given that the mean (\(\mu\)) is 195 pages and the standard deviation (\(\sigma\)) is 25 pages, we are asked to find the probability that a randomly selected book has fewer than 170 pages.

Step 2 ：We first standardize the value 170 by subtracting the mean and dividing by the standard deviation. This gives us the z-score, which represents how many standard deviations away from the mean our value is.

Step 3 ：\(z = \frac{170 - 195}{25} = -1.0\)

Step 4 ：The z-score is -1, which means the value 170 is one standard deviation below the mean.

Step 5 ：According to the empirical rule, 68% of data falls within one standard deviation, so 32% falls outside, and half of that is 16%. Therefore, the probability of a randomly selected book having fewer than 170 pages is approximately 16%.

Step 6 ：Final Answer: The probability that a randomly selected book has fewer than 170 pages is approximately \(\boxed{16\%}\).