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Shelia does quality control for a company that manufactures lawn mower parts. On any given day, she finds the probability distribution for defective parts as shown in the table.

Using the data from the table, what is the probability of having 2 defective parts in a day?

\begin{tabular}{|c|c|}
\hline
Defective Parts: [tex]$X$[/tex] & Probability: [tex]$P(X)$[/tex] \\
\hline
0 & 0.85 \\
\hline
1 & 0.10 \\
\hline
2 & 0.04 \\
\hline
3 & 0.01 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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]