Question
Download Solution PDFFor a standard normal probability distribution, the mean (μ) and the standard deviation (s) are :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe simplest case of a normal distribution is known as the standard normal distribution. This is a special case when μ = 0 and σ = 1, and it is described by this probability density function:
\(ϕ (x) = \dfrac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}\)
Here, the factor \(1/\sqrt{2\pi}\) ensures that the total area under the curve ϕ(x) is equal to one. The factor 1/2 in the exponent ensures that the distribution has unit variance (i.e., variance being equal to one), and therefore also unit standard deviation. This function is symmetric around x = 0, where it attains its maximum value \(1/\sqrt{2\pi}\) and has inflection points at x = +1 and x = -1.
Thus, option 1 is the correct answer.
Last updated on Jun 6, 2025
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