The function f(x) represents a normal distribution whose standard deviation and mean are 1 and 5, respectively. The value of f(x) at x = 5 is
Options:
(A) 0.0
(B) 0.159
(C) 0.282
(D) 0.398
Official Answer Key:
D
Step-by-Step Solution & Explanation
For a normal density f(x) = 1/(σ√(2π)) · exp[−(x−μ)²/2σ²], at x = μ the exponential term is 1, so f(μ) = 1/(σ√(2π)) = 1/(1×2.5066) = 0.3989 ≈ 0.398 → option (D). This is the well-known peak value of the standard normal density. Option (B) 0.159 is 1/(2π) with the wrong exponent handling; (C) is unrelated.
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