GATE AG 2014 • Q39 MCQ • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

If f(x) is a normal distribution with mean 8 and standard deviation 1, the value of f(x) for x = 10 is

Options:

  • (A) 0.05
  • (B) 0.14
  • (C) 0.25
  • (D) 0.73

Official Answer Key:

A

Step-by-Step Solution & Explanation

Normal PDF: f(x) = (1/σ√(2π)) exp[−(x−μ)²/2σ²], with μ=8, σ=1. z = (x−μ)/σ = (10−8)/1 = 2. f(x) = (1/√(2π)) e⁻² = 0.39894 × 0.13534 = 0.0540 ≈ 0.05. Answer: (A).

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