To determine the approximate value of \( P(z \leq 0.42) \) for a standard normal distribution, we refer to the standard normal table provided. The standard normal table gives the cumulative probability for a given z-value.
Here are the steps:
1. Identify the z-value for which we need to find the cumulative probability. In this case, the z-value is \( z = 0.42 \).
2. Look up the corresponding cumulative probability in the standard normal table. According to the given portion of the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
[tex]$z$[/tex] & Probability \\
\hline
0.00 & 0.5000 \\
\hline
0.22 & 0.5871 \\
\hline
0.32 & 0.6255 \\
\hline
0.42 & 0.6628 \\
\hline
0.44 & 0.6700 \\
\hline
0.64 & 0.7389 \\
\hline
0.84 & 0.7995 \\
\hline
1.00 & 0.8413 \\
\hline
\end{tabular}
\][/tex]
From the table, we see that the cumulative probability corresponding to \( z = 0.42 \) is \( 0.6628 \).
Therefore, the approximate value of \( P(z \leq 0.42) \) is \( 0.6628 \).
So, from the given options, the choice that represents this value most accurately in percentage terms is [tex]\( 66\% \)[/tex].
