To solve this problem, we need to identify the correct rows that represent valid probability distributions for the amount paid for lunch by students in the given county. Let's assess each row based on the given probabilities and prices:
- [tex]\( x = 1.50, P(X) = 0.28 \)[/tex]
The amount paid is [tex]\( \$1.50 \)[/tex], and the probability is [tex]\( 0.28 \)[/tex] (or 28%). This aligns with the given information: 28% of students receive reduced fee lunch, so this row is correct.
- [tex]\( X = 3.50, P(X) = 0.39 \)[/tex]
The amount paid is [tex]\( \$3.50 \)[/tex], and the probability is [tex]\( 0.39 \)[/tex] (or 39%). This matches the given fact that 39% of students pay full price for lunch, making this row correct.
- [tex]\( x = 3.50, P(X) = 39 \)[/tex]
Here, the amount paid is [tex]\( \$3.50 \)[/tex], but the probability is incorrectly stated as [tex]\( 39 \)[/tex]. Probabilities must be a value between 0 and 1, so this row cannot be correct.
- [tex]\( x = 39, P(X) = 3.50 \)[/tex]
This row states that [tex]\( x = 39 \)[/tex] (presumably dollars) for lunch, with a probability of [tex]\( 3.50 \)[/tex]. Again, this isn't valid since probabilities must be between 0 and 1. Thus, this row is incorrect.
Therefore, the correct rows that can be included in the probability distribution for [tex]\( X \)[/tex], where [tex]\( X \)[/tex] represents the amount paid for lunch, are:
[tex]\[
\begin{aligned}
&x = 1.50, P(X) = 0.28 \\
&X = 3.50, P(X) = 0.39
\end{aligned}
\][/tex]
Hence, these are the correct rows.
