Question

X ~ N (100, 15) is read as

• A. X is a normal random variable with median 100 and standard deviation 15
• B. X is a normal random variable with mean 100 and standard deviation 15
• C. X is a normal random variable with mode 100 and variance 15
• D. X is a normal random variable with mean 100 and variance 15

Hint:

Statistical Notation: $X \sim N(\mu, \sigma)$ $\rightarrow$ Normal distribution with Mean $\mu$ and Standard Deviation $\sigma$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Standard notation for the univariate Gaussian normal distribution: $X \sim N(\mu, \sigma)$ specifies a normally distributed random variable $X$ with location parameter mean $\mu$ and scale parameter standard deviation $\sigma$.
Key Formula or Approach:
\[ X \sim N(\mu, \sigma^2) \quad \text{or} \quad X \sim N(\mu, \sigma) \implies \mu = \text{Mean} = 100, \quad \sigma = \text{Standard Deviation} = 15 \]

Step 2: Detailed Explanation:
In statistical theory and distribution notation:
- The standard shorthand notation \( X \sim N(\mu, \sigma) \) signifies that:
1. The random variable \( X \) follows a Normal (Gaussian) Distribution.
2. The first parameter \( \mu = 100 \) represents the Population Mean.
3. The second parameter \( 15 \) represents the Standard Deviation ($\sigma = 15$).
- Therefore, the expression is read as: '$X$ is a normal random variable with mean 100 and standard deviation 15'.

Step 3: Final Answer:
Therefore, X ~ N(100, 15) is read as X is a normal random variable with mean 100 and standard deviation 15, corresponding to option (B).