Question

Which of the following is not a characteristic of the normal distribution ?

• A. the mean is always zero
• B. the area under the curve equals one
• C. the mean, median and mode are equal
• D. it is a symmetrical distribution

Hint:

Remember:
- Normal Distribution: Mean = $\mu$, SD = $\sigma$
- Standard Normal Distribution: Mean = $0$, SD = $1$
Do not confuse the general distribution with its standardized form.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The normal distribution is a continuous probability distribution defined by two parameters: the mean ($\mu$) and the variance ($\sigma^2$).
We must distinguish between the general normal distribution $N(\mu, \sigma^2)$ and the Standard Normal Distribution $N(0, 1)$.
Detailed Explanation:
Let us evaluate each characteristic:
- (A) The mean is always zero: This is incorrect. A general normal distribution can have any real number as its mean ($\mu \in \mathbb{R}$). Only the *Standard Normal Distribution* has a mean of exactly zero. Thus, this is not a general characteristic.
- (B) The area under the curve equals one: This is correct. Because it is a probability density function, the total area under the entire normal curve must equal 1.
- (C) The mean, median, and mode are equal: This is correct. The normal distribution is unimodal and symmetric around its center, so the mean, median, and mode coincide at the peak of the curve.
- (D) It is a symmetrical distribution: This is correct. The normal distribution is perfectly symmetric about its mean.

Step 2: Final Answer:
The statement that is not a characteristic is Option (A).