(1)   Normal distribution was first derived by De - movire in 1973 , who was a British Mathematician .

(2)    Normal distribution is also known as Gaussian distribution , named after Karl Friedrich Gauss ,That is why it is also known as gaussian distribution .

(3)    This is most important and globally accepted continuous probability distribution in statistical analysis.

(4)    A continuous random variable x is said to have normal distribution with mean μ and variance (SD)² if its probability density function is given by .

f(x) =

1/SD√(2π)

e^{-{(x - μ)2}/2SD2} , - ∞ ≤ x ≤ ∞
SD > 0
= 0 ; otherwise

It is denoted x ∿ N (μ , SD²)

(5)    It is bell shaped curve , symmetrical about mean .

(6)    In this distribution mean = median = mode .

(7)    The curve is asymptotic to x - axis, as the left tail and right tail never touch the horizontal axis (x - axis) .

(8)   The normal curve has one peak , has unique mode .

(9)    Quartiles are equidistant from median , so median is =

Q₃ + Q₁/2

.

(10)   Normal distribution is bi - parametric distribution,its parameter are μ and SD² .

(11)    Point of inflexion of the curve are μ ± SD

(12)    Total area under normal curve is 1 .
(a)    Area between μ ± 1,96 SD = 0.95
(b)    Area between μ ± 2.58 SD = 0.99
(c)   Area between μ ± SD = 0.6826 .
(d)    Area between μ ± 2SD = 0.9545 .
(d)    Area between μ ± 3 SD = 0.9973

(13)   Mean Deviation of normal distribution is M.D = SD√(2π) = (4/5)SD = 0.8 SD

(14)    In this distribution ,
lower quartile (Q₁) = μ - 0.675 SD
Upper quartile (Q₂) = μ + 0.675 SD
and Quartile deviation is 0.675 SD .

(15)    In normal distribution ,
Q.D : M.D : S.D = 10 : 12 : 15

(16)    If x and y are independent normal variables with means and standard deviations as μ₁ and μ₂ respectively . then x + y will follow normal distribution with mean (μ₁ + μ₂) and standard deviation √(SD₁² + SD₂ ²) respectively .

If x ∿ N (μ₁, SD₁²)

y ∿ N(μ ₂, SD₂ ² )

where x and y are independent .
then (x + y) ∿ N(μ₁ + μ₂ , SD₁² + SD₂² ) .