710. Generate four possible values of a normal random variable with parameters: a) $a=0, \sigma=1$; b) $a=2, \sigma=3$.
Solution. a) In accordance with the rule, let's determine the possible value of $x_{1}$ of the normal random variable $X$ with parameters $a=0$ and $\sigma=1$ using the formula

$$
x_{1}=\sum_{i=1}^{12} r_{j}-6=S_{1}-6
$$

Select the first 12 random numbers from the second row of the table in Appendix 9: 0.37; 0.54; 0.20; 0.48; 0.05; 0.64; 0.89; 0.47; 0.42; 0.96; 0.24; 0.80. Adding these numbers, we get $S_{i}=6.06$. The sought possible value $x_{1}=S_{1}-6=6.06-6=0.06$.

Similarly, selecting the first 12 random numbers from the third, fourth, and fifth rows of the table, we get: $S_{2}=4.90, S_{3}=4.48$, $S_{4}=6.83$. Therefore, $x_{2}=4.90-6=-1.10; x_{3}=4.48-6=-1.52$; $x_{4}=6.83-6=0.83$.

6) Let's find the possible values of the normal random variable $Z$ with parameters $a=2, \sigma=3$ using the formula $z_{i}=\sigma x_{i}+a$. Substituting the possible values $x_{i}=0.06, a=2, \sigma=3$, we get $z_{1}=3 \cdot 0.06+2=2.18$.

Similarly, we will find the other possible values: $z_{2}=-1.3$, $z_{3}=-2.56, z_{4}=4.49$.