Final answer:
All statements about the normal distribution being symmetric, specified by a mean and a standard deviation, and having an area under the curve of exactly 1 are true; hence, the correct answer is that all options provided are correct.
Step-by-step explanation:
The question asks whether a normal distribution is symmetric, can be completely specified by a mean and a standard deviation, and has an area of exactly 1 underneath the density curve. The options provided in the question suggest that all of these statements may be considered collectively.
The normal distribution is indeed symmetric about the mean, and it can be completely described by two parameters - the mean (μ) and the standard deviation (σ). This distribution is commonly represented as a bell-shaped curve, with the mean, median, and mode all being equivalent and located at the peak of the bell. Additionally, a key property of the normal distribution is that the total area under the curve is equal to 1, which represents the entire probability space.
Therefore, the correct answer to the question is d. all of the answers, implicating that all the statements a, b, and c are correct descriptions of a normal distribution.