68.27% of area lie between x = - 1σ to x = +1σ
95.45% of area lie between x = - 2σ to x = +2σ
99.73% of area lie between x = - 3σ to x = +3σ
10 . x can lie anywhere between - infinity to + infinity .
11 . if we take( x - m ) / σ = z , then
P(x) = ( 1 / σ*√[2π] ) e -z*z;/2
Properties of Standard Normal Distribution
1 . mean =μ= 0 ; σ = 1
2.P(x) = ( 1/√[2π]) e- z*z/2
3 .∫
P(x) dx = 1 where limit is from -infinity to +infinity. The integral does not
have a closed formula but has to be numerically computed The largest value of the function is inversely proportional to standard
deviation
σ
4. The Normal/Gaussian distribution is the limit of Binomial
distribution when sample size n approaches infinity. Otherwise, when value
of p and q in the binomial are close to 0.5, it can be approximated to a
gaussian distribution with finite small sample size.