GATE AG 2008 • Q1 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

If f(x) is a perfect normal distribution with mean and standard deviation of 5 and 1 respectively, then the value of f(x) for x = 6 is

Options:

  • (A) 0.124
  • (B) 0.242
  • (C) 0.482
  • (D) 0.524

Official Answer Key:

B

Step-by-Step Solution & Explanation

Normal PDF: f(x) = 1/(σ√(2π)) · exp(−(x−μ)²/2σ²). With μ=5, σ=1, x=6: f(6) = (1/√(2π))·exp(−0.5) = 0.39894 × 0.60653 = 0.2420. Option (A) is a common slip from using the wrong exponent sign; (D) mistakes the standard normal ordinate at z=0.

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