Allied & ICAR Exam Bank • ALLIED_1017NAT • 2 Marks
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Normal distribution
Question Statement:
A continuous random variable $X$ is normally distributed with mean $\mu = 50$ and standard deviation $\sigma = 10$. The percentage of values expected to lie in the range $[30, 70]$ (within $\pm 2\sigma$) according to the empirical rule is approximately:
Answer Key:
95.4
Step-by-Step Solution & Explanation
For a normal distribution, the probability of lying within $\pm 2$ standard deviations of the mean $(\mu - 2\sigma \le X \le \mu + 2\sigma)$ is $2 \Phi(2) - 1 \approx 2(0.9772) - 1 = 0.9544$ or $95.44\%$.