[tex]\[
\begin{array}{|c|c|}
\hline
z & \text{Probability} \\
\hline
0.00 & 0.5000 \\
\hline
1.00 & 0.8413 \\
\hline
2.00 & 0.9772 \\
\hline
3.00 & 0.9987 \\
\hline
\end{array}
\][/tex]



Answer :

To understand how we arrive at the provided result, let us break it down step-by-step.

Given a table that lists z-values and their corresponding probabilities:

[tex]\[ \begin{array}{|c|c|} \hline z & \text{Probability} \\ \hline 0.00 & 0.5000 \\ \hline 1.00 & 0.8413 \\ \hline 2.00 & 0.9772 \\ \hline 3.00 & 0.9987 \\ \hline \end{array} \][/tex]

We are expected to determine two lists:
1. An ordered list of the given probabilities.
2. A provided list of probabilities to search for: 0.02, 0.16, 0.18, and 0.82.

By parsing the table, we can extract the list of probabilities in the original order they appear:
[tex]\[ [0.5000, 0.8413, 0.9772, 0.9987] \][/tex]

These are the probabilities associated with z-values of 0.00, 1.00, 2.00, and 3.00 respectively.

Next, we are given another list of probabilities to search for:
[tex]\[ [0.02, 0.16, 0.18, 0.82] \][/tex]

There is no need for additional calculations or look-up processes for these values; we simply list them as given.

Thus, our ordered list of probabilities derived from the table is:
[tex]\[ [0.5000, 0.8413, 0.9772, 0.9987] \][/tex]

And the provided list of probabilities to search for is:
[tex]\[ [0.02, 0.16, 0.18, 0.82] \][/tex]

Therefore, the complete answer to the problem can be written as:
[tex]\[ ([0.5000, 0.8413, 0.9772, 0.9987], [0.02, 0.16, 0.18, 0.82]) \][/tex]