<Dl> <Dd> f (x) = e a x 2 + b x + c (\ displaystyle f (x) = e ^ (ax ^ (2) + bx + c)) </Dd> </Dl> <Dd> f (x) = e a x 2 + b x + c (\ displaystyle f (x) = e ^ (ax ^ (2) + bx + c)) </Dd> <P> where a <0 (\ displaystyle a <0) and c = b 2 / (4 a) + ln ⁡ (− a / π) / 2 (\ displaystyle c = b ^ (2) / (4a) + \ ln (- a / \ pi) / 2). In this form, the mean value is μ = − b / (2 a) (\ displaystyle \ mu = - b / (2a)), and the variance is σ 2 = − 1 / (2 a) (\ displaystyle \ sigma ^ (2) = - 1 / (2a)). For the standard normal distribution, a = − 1 / 2 (\ displaystyle a = - 1 / 2), b = 0 (\ displaystyle b = 0), and c = − ln ⁡ (2 π) / 2 (\ displaystyle c = - \ ln (2 \ pi) / 2). </P> <P> The probability density of the standard Gaussian distribution (standard normal distribution) (with zero mean and unit variance) is often denoted with the Greek letter φ (\ displaystyle \ phi) (phi). The alternative form of the Greek letter phi, φ (\ displaystyle \ varphi), is also used quite often . </P>

When is data said to be normally distributed