Question

a teacher assigns a score from 1 to 4 to each student project. the table below shows the probability distribution of the scores for a randomly selected student. which score is most likely?

probability distribution
score: x | probability: p(x)
1 | 0.06
2 | 0.20
3 | 0.48
4 | 0.26

1
2
3
4

Explanation:

Identify the probabilities for each score

The table lists the probability \(P(X)\) for each score \(X\):

• For \(X = 1\), \(P(1) = 0.06\)
• For \(X = 2\), \(P(2) = 0.20\)
• For \(X = 3\), \(P(3) = 0.48\)
• For \(X = 4\), \(P(4) = 0.26\)

Compare the probabilities to find the maximum

Comparing the values:

$$ 0.48 > 0.26 > 0.20 > 0.06 $$

The highest probability is \(0.48\), which corresponds to a score of \(3\).

Determine the most likely score

Since a score of \(3\) has the highest probability, it is the most likely score.

Answer:

• 1
• 2
• 3 (Correct answer)
• 4