An example given in context of simple random sampling, says - We have five random numbers $\mathrm{9792, 1396, 2762, 6107, 9025}$. Obtain a random sample of size $\mathrm{5}$ from normal population $\mathcal{N(0,1)}$
Hence we have the pdf $$\mathrm{\phi(z)=\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}z^2}};\ \ \ \ \ \mathrm{-\infty<z<\infty}$$
Now using those five given random numbers we have
$$\mathbb{P}\mathrm{(Z\leq z_i)=10^{-k}\times[\textrm{ k - digit random number }]} \\ \textrm{Hence for i = 1,2,3,4,5 we have; }\\ \mathbb{P}\mathrm{(Z\leq z_1)=10^{-4}\times[ 9792]=0.9792}, \\ \mathbb{P}\mathrm{(Z\leq z_2)=10^{-4}\times[ 1396]=0.1396}\\\mathbb{P}\mathrm{(Z\leq z_3)=10^{-4}\times[ 2762]=0.2762}\\\mathbb{P}\mathrm{(Z\leq z_4)=10^{-4}\times[ 6107]=0.6107}\\\mathbb{P}\mathrm{(Z\leq z_5)=10^{-4}\times[ 9025]=0.9025}$$
Now here is the part that I did not understand how to calculate and even after reading probability distributions and raandom sampling basics I do not have any clue of calculation.
The example says that $$\mathbb{P}\mathrm{(0\leq Z\leq z_1)=0.4792} \ \textrm{ and }\ \mathrm{z_1=2.04} \textrm{ , from normal table }\\ \mathbb{P}\mathrm{(0\leq Z\leq z_{2}^{'})=0.3794} \ \textrm{ and }\ \mathrm{z_{2}=-1.13} \textrm{ , from normal table }\\\mathbb{P}\mathrm{(0\leq Z\leq z_{3}^{'})=0.2238} \ \textrm{ and }\ \mathrm{z_{3}=-0.59} \textrm{ , from normal table }\\\mathbb{P}\mathrm{(0\leq Z\leq z_4)=0.1107} \ \textrm{ and }\ \mathrm{z_4=0.28} \textrm{ , from normal table }\\\mathbb{P}\mathrm{(0\leq Z\leq z_5)=0.4025} \ \textrm{ and }\ \mathrm{z_5=1.30} \textrm{ , from normal table }\\ $$
$\textrm{My questions}$
$\triangle_{1}:$ Why do $\mathbb{P}\mathrm{(Z\leq z_i)} \ \textrm{ and }\ \mathbb{P}\mathrm{(0\leq Z\leq z_i)}$ differ for $\mathrm{i=1,2,3,4,5}$ and how do we calculate the $\mathbb{P}\mathrm{(0\leq Z\leq z_i)}$?
$\triangle_{2}:$ Here $\mathrm{z_2=-z_{2}^{'}, z_3=-z_{3}^{'}}$, due to symmetry. But how do we use $z_{i}^{'}$ in the integration for $\textrm{i=2,3}$?
$\triangle_{2}:$ Can random sample units be negative (like $\mathrm{z_2, z_3})$?
Any help, explanations are valuable and much appreciated.