To determine the probability of having exactly 2 defective parts in a day, you need to refer to the provided probability distribution table. The table lists the number of defective parts [tex]\( X \)[/tex] and their corresponding probabilities [tex]\( P(X) \)[/tex].
Here's the table for reference:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Defective Parts: } X & \text{Probability: } P(X) \\
\hline
0 & 0.85 \\
\hline
1 & 0.10 \\
\hline
2 & 0.04 \\
\hline
3 & 0.01 \\
\hline
\end{tabular}
\][/tex]
To find the probability that Shelia encounters exactly 2 defective parts on a given day:
1. Identify the row in the table where [tex]\( X = 2 \)[/tex].
2. Look at the corresponding probability value [tex]\( P(X = 2) \)[/tex].
From the table:
[tex]\[
P(X = 2) = 0.04
\][/tex]
Therefore, the probability of having 2 defective parts in a day is:
[tex]\[
\boxed{0.04}
\][/tex]
