Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
A normal random variable has mean equal to 0, and standard deviation equal to 3.
The probability that on a random draw the value of this random variable is greater
than 0 is
(round off to 2 decimal places).
Official Answer Key:
0.49 to 0.51
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2020 Q.34)**
**1. Governing Concept & Definition**:
- **Topic**: Probability & Normal Distribution Symmetry
- A normal random variable $X \sim \mathcal{N}(\mu, \sigma^2)$ is symmetric about its mean $\mu$:
$P(X \ge \mu) = P(X \le \mu) = 0.5$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Mean $\mu = 0$
- Standard deviation $\sigma = 3$
- **Target Probability**: Probability that on a random draw, $X \ge 0$ (or $X \le 0$):
$P(X \ge 0) = 0.50$
**3. Final Answer**:
- **Calculated Value**: **0.50**
- **Official GATE Accepted Range**: **0.49 to 0.51**
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