The correct answer is: A. The normal distribution is asymmetric and peaked about its mode.
The normal distribution is a continuous probability distribution that is often used to model real-world data. It is characterized by a bell-shaped curve, with the mode (the most likely value) located at the center of the curve. The mean, median, and mode are all equal for a normal distribution.
A constant times a normally distributed random variable is also normally distributed. This is because the normal distribution is a linear function. If you multiply a normally distributed random variable by a constant, the resulting random variable will also be normally distributed.
Sample means of normally distributed random variables are again normally distributed. This is known as the central limit theorem. The central limit theorem states that, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the underlying distribution of the population.
Therefore, the only statement that is incorrect is A. The normal distribution is asymmetric and peaked about its mode.