Normal Distribution

Normal Distribution

X~N(μ,σ^2) The mean μ is always in the middle The graph is symmetrical about the middle The larger the value of σ^2 the more flat the curve The area between the curve and the x-axis is the probability P(X=a)=0 https://www.mathsisfun.com/data/standard-normal-distribution.html

Gaussian Labeled 2x B95dbf3b 42f2 44b8 8034 88835c10b3e4 (image/png)

Caption: : A Bell Curve Graph

Standard Normal

Let Z be a Continuous Random Variable that is Normally Distributed with μ=0 and unit variance (σ^2), then Z is the Standard Normal∴ Z~N(0,1)Use Table 7 in Stats Booklet

Non-Standard Normal

Z=X-μ/σ  ⇒  Z~N(0,1)NB: Divide by Standard Deviation

EquationsP(Z>a)=Q(a)P(Z<a)=1-Q(a)P(Z>-a)=1-Q(a)P(Z<-a)=Q(a)P(a<Z<b)=Q(a)-Q(b)P(-a<Q<b)=1-Q(b)-Q(a)P(-a<Z<-b)=Q(b)-Q(a)