Subtopic: Poisson, normal and binomial distributions
Question Statement:
Which of the following are TRUE properties of a standard Normal distribution $Z \sim \mathcal{N}(0, 1)$?
Options:
(A) The probability density function is symmetric about $z = 0$.
(B) Mean, median, and mode are all equal to 0.
(C) The total area under the probability density curve is equal to 1.
(D) The variance of the distribution is 2.
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
For the standard normal distribution $\mathcal{N}(0, 1)$, the curve is symmetric about mean $\mu = 0$, so mean $=$ median $=$ mode $= 0$. Total probability area $= 1$. Statement D is false because standard normal variance $\sigma^2 = 1$, not 2.