Normal

dist = NormalDistribution[μ,σ]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[NormalDistribution[μ,σ],z],{z,-6,6},Filling->Axis],{μ,1,2},{σ,1,2}]

Manipulate[Plot[Table[PDF[NormalDistribution[μ,σ],z],{σ,{.75,1,2}}]//Evaluate,{z,-6,6},Filling->Axis],{μ,1,2}]

Manipulate[Plot[Table[PDF[NormalDistribution[μ,σ],z],{μ,{-1,1,2}}]//Evaluate,{z,-6,6},Filling->Axis],{σ,1,2}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[NormalDistribution[0,1]]