Final answer:
To find a and -a such that p(a < z < -a) = 0.99 in a normal distribution, you use a z-table to find the z-score with 0.995 to the left, resulting in a and -a being approximately 2.576.
Step-by-step explanation:
The student's question is concerning the normal distribution and finding symmetric points (a and -a) about the mean where the probability between them is 0.99. To solve this, one generally uses a z-table or a calculator to find the z-score that captures the central portion of the probability under the standard normal curve.
Given that p(a < z < -a) = 0.99, we understand that we are dealing with a two-tailed test since a and -a represent bounds on opposite sides of the mean. Therefore, the total area in the two tails is 1 - 0.99 = 0.01, which means there's 0.005 in each tail. Using a z-table, a calculator, or statistical software, we find the z-score such that the area to the right is 0.005. The z-score that corresponds to 0.995 (0.5 + 0.495) on the standard normal distribution is approximately 2.576.
The values of a and -a will then both be approximately 2.576, indicating that the interval (-a, a) captures 99% of the probability in a standard normal distribution.