The test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution, as shown in the figure.
(a) What is the maximum score that can be in the bottom $15 \%$ of scores?
(b) Between what two values does the middle $70 \%$ of scores lie?
(a) The maximum score that can be in the bottom $15 \%$ is (Round to two decimal places as needed.)

Step 1 ：We are given that the test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution.

Step 2 ：We need to find the maximum score that can be in the bottom 15% of scores. This is equivalent to finding the z-score for which the cumulative distribution function (CDF) is 0.15.

Step 3 ：A z-score is a measure of how many standard deviations an element is from the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 4 ：We can use statistical methods to find this z-score. The z-score corresponding to the bottom 15% of scores is approximately -1.0364333894937898.

Step 5 ：We then need to convert this z-score to a test score. If we assume that the mean score is 0 and the standard deviation is 1 (as is standard in a normal distribution), then the test score corresponding to a given z-score is simply the z-score itself.

Step 6 ：However, if the mean and standard deviation of the test scores are not 0 and 1, respectively, we would need to multiply the z-score by the standard deviation and add the mean to get the corresponding test score.

Step 7 ：Assuming that the mean score is 0 and the standard deviation is 1, the maximum score that can be in the bottom 15% of scores is approximately -1.04 (rounded to two decimal places).

Step 8 ：Final Answer: The maximum score that can be in the bottom 15% of scores is approximately \(\boxed{-1.04}\).