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]
