Question

The coefficient of skewness for a normal distribution is

• A. +1
• B. -1
• C. 3
• D. 0

Hint:

Normal Distribution Parameters:
Skewness = 0 (Symmetric).
Kurtosis ($\beta_2$) = 3 (Mesokurtic).
Mean = Median = Mode.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Moments of the Gaussian normal distribution: perfect bilateral symmetry around the central mean ($\mu = ext{Median} = ext{Mode}$) results in an exact third standardized moment (skewness $\gamma_1$) of zero.
Key Formula or Approach:
\[ \text{Skewness } (\gamma_1) = \frac{\mu_3}{\sigma^3} = \frac{\text{Mean} - \text{Mode}}{\sigma} = 0 \quad (\text{Kurtosis } \beta_2 = 3) \]

Step 2: Detailed Explanation:
In statistical probability theory:
- A Normal (Gaussian) Distribution is perfectly symmetrical and bell-shaped around its central location parameter:
1. \(\text{Mean} = \text{Median} = \text{Mode}\).
2. Coefficient of Skewness ($\gamma_1$ $\sqrt{\beta_1}$): Measures asymmetry of probability distribution; for a normal distribution, Skewness = 0 (Zero) (D).
3. Kurtosis ($\beta_2$): Measures peakedness; for a normal distribution, $\beta_2 = 3$ (mesokurtic excess kurtosis = $0$).

Step 3: Final Answer:
Thus, the coefficient of skewness for a normal distribution is 0, matching option (D).