🔗 Definition 5.6.1. Conversion to Standard Units. 🔗 🔗Any distribution variable can be converted to “standard units” using the linear translation z=x−μσ. 🔗In doing so, values of z will always represent the number of standard deviations x is from the mean and will provide “dimensionless” comparisons.
Consider our earlier continuous example 5.4.4 in which we found μ=54 and .σ=5180. Then, P(0<X<1)=P(0−545180<X−545180<1−545180) gives the middle term is Z and the other endpoints are now in standard units that indicate the number of standard deviations from the mean rather than actual problem units.
