Consider a data set $X$ made up of smaller subsets: $X=A \cup B \cup C$, with $A,B,C$ disjoint data sets. Eg: $A=\{1.0, -1.0, 0\}$, $B=\{5.0, -7.0, 2.0\}$, $C=\{1.5, -5.0, 8.0\}$
Is is possible to transform (scale, shift) $A,B,C$ such that each is individually standard normally distributed (mean=0standardised to have mean=0, stdand std dev=1.0), and so that $X$ is also standard normally distributedhas mean=0, std dev=1.0?