Compute PDF, CDF, and inverse CDF for the normal (Gaussian) distribution with given μ and σ.
The normal (Gaussian) distribution is the most important continuous distribution in statistics. It is completely defined by its mean μ and standard deviation σ. About 68% of values lie within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ.
f(x) = (1/(σ√(2π))) × exp(−(x−μ)²/(2σ²))
Standard Z
z = (x − μ) / σ
It is the normal distribution with μ = 0 and σ = 1. Any normal variable can be converted to standard normal using z = (x − μ)/σ.
The Central Limit Theorem states that the sum (or mean) of many independent random variables tends toward a normal distribution regardless of the underlying distribution.