Sure, let's solve this problem step by step. We want to find the probability of having exactly 2 defective parts in a day based on the provided probability distribution.
1. Understanding the problem:
- The quality control data provides us with probabilities for different numbers of defective parts (0, 1, or 2) on any given day.
2. Probability Distribution Table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Defective Parts (X)} & \text{Probability (P(X))} \\
\hline
0 & 0.85 \\
\hline
1 & 0.10 \\
\hline
2 & 0.04 \\
\hline
\end{tabular}
\][/tex]
3. Finding the desired probability:
- We need the probability for the event where the number of defective parts, [tex]\(X\)[/tex], equals 2.
- From the table, we look for the probability that corresponds to [tex]\(X = 2\)[/tex].
4. Extracting the probability:
- According to the table, the probability [tex]\(P(X = 2)\)[/tex] is given as 0.04.
Therefore, the probability of having 2 defective parts in a day is [tex]\(0.04\)[/tex].
