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 \(\boxed{16\%}\).