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
• 
• 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
• Equations
• P(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)