To determine the median of the given probability distribution, we'll follow these steps:
1. List the tickets and their corresponding probabilities:
[tex]\[
\begin{array}{c|c}
\text{Number of Tickets (X)} & \text{Probability} \\
\hline
1 & 0.29 \\
2 & 0.44 \\
3 & 0.19 \\
4 & 0.06 \\
5 & 0.02 \\
\end{array}
\][/tex]
2. Find the cumulative distribution:
Compute the cumulative probabilities by adding the probabilities sequentially:
[tex]\[
\begin{array}{c|c|c}
\text{Number of Tickets (X)} & \text{Probability} & \text{Cumulative Probability} \\
\hline
1 & 0.29 & 0.29 \\
2 & 0.44 & 0.29 + 0.44 = 0.73 \\
3 & 0.19 & 0.73 + 0.19 = 0.92 \\
4 & 0.06 & 0.92 + 0.06 = 0.98 \\
5 & 0.02 & 0.98 + 0.02 = 1.00 \\
\end{array}
\][/tex]
This gives us the cumulative distribution:
[tex]\[
[0.29, 0.73, 0.92, 0.98, 1.00]
\][/tex]
3. Determine the median:
The median is the point at which the cumulative probability reaches or exceeds 0.5. From the cumulative distribution:
[tex]\[
\begin{array}{c|c}
\text{Number of Tickets (X)} & \text{Cumulative Probability} \\
\hline
1 & 0.29 \\
2 & 0.73 \\
3 & 0.92 \\
4 & 0.98 \\
5 & 1.0 \\
\end{array}
\][/tex]
We see that at [tex]\(X = 2\)[/tex], the cumulative probability is 0.73, which is the first value greater than or equal to 0.5.
Therefore, the median of the distribution is 2.
