Question Bank • QB_EM_126 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

A normal distribution has mean $\mu = 50$ and standard deviation $\sigma = 10$. If the standardized normal score $Z = \frac{X - \mu}{\sigma}$ corresponding to a value $X$ is $1.5$, calculate the value of $X$.

Answer Key:

65

Step-by-Step Solution & Explanation

$Z = \frac{X - \mu}{\sigma} \implies X = \mu + Z \sigma = 50 + (1.5 \times 10) = 50 + 15 = 65.0$
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