5.5.1—Normal distribution

X~N(μ,σ²) is centred at μ with standard deviation σ. Standardise using Z=(X−μ)/σ, where Z~N(0,1), then use symmetry or normal tables/calculator.

State whether a probability is a lower tail, upper tail or interval. A continuous variable has P(X=a)=0, so endpoint inclusion does not change a probability.

For X~N(10,4), P(X<12)=P(Z<1)=0.8413.

σ is the standard deviation, not the variance; writing N(μ,σ) in a convention that expects variance changes the model.