To determine which score is most likely, we need to examine the provided probability distribution for the scores assigned to student projects. The probability distribution indicates the likelihood of each score (from 1 to 4) being assigned.
Here is the table given in the problem:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{ Probability Distribution } \\
\hline
Score: \, X & Probability: \, P(X) \\
\hline
1 & 0.06 \\
\hline
2 & 0.20 \\
\hline
3 & 0.48 \\
\hline
4 & 0.26 \\
\hline
\end{tabular}
\][/tex]
1. Understand the Table: Each row in the table shows a score and the probability of that score being assigned.
2. Identify Highest Probability: To find the most likely score, we need to identify the score with the highest probability, [tex]\( P(X) \)[/tex].
- Score 1 has a probability of 0.06
- Score 2 has a probability of 0.20
- Score 3 has a probability of 0.48
- Score 4 has a probability of 0.26
3. Compare Probabilities:
- For Score 1: [tex]\( P(1) = 0.06 \)[/tex]
- For Score 2: [tex]\( P(2) = 0.20 \)[/tex]
- For Score 3: [tex]\( P(3) = 0.48 \)[/tex]
- For Score 4: [tex]\( P(4) = 0.26 \)[/tex]
4. Determine the Maximum Probability: Out of these probabilities, 0.06, 0.20, 0.48, and 0.26, the highest value is 0.48.
5. Associate the Highest Probability with the Correct Score: The probability 0.48 corresponds to Score 3.
Thus, the most likely score to be assigned to a randomly selected student project is 3.
