To determine the correct interpretation of [tex]\( P(X > 4) \)[/tex] using the given distribution of scores and their probabilities, we need to follow these steps:
1. Identify the possible scores and their corresponding probabilities:
- Score 1: Probability 0.18
- Score 2: Probability 0.20
- Score 3: Probability 0.26
- Score 4: Probability 0.21
- Score 5: Probability 0.15
2. Focus on the condition [tex]\( X > 4 \)[/tex]:
- A score greater than 4 can only be a score of 5 in this distribution.
3. Extract the probability of a score of 5:
- The probability of getting a score of 5 is 0.15.
Therefore, [tex]\( P(X > 4) \)[/tex] is 0.15.
With this information, let's analyze the given interpretations:
1. The probability of a randomly selected test having a score of at most 4 is 0.36.
- This is incorrect. The probability of scoring at most 4 includes the sum of the probabilities for scores 1, 2, 3, and 4.
2. The probability of a randomly selected test having a score of at least 4 is 0.36.
- This is incorrect. The probability of scoring at least 4 includes the sum of probabilities for scores 4 and 5.
3. The probability of a randomly selected test having a score lower than 4 is 0.85.
- This is incorrect. The probability of scoring lower than 4 includes the sum of probabilities for scores 1, 2, and 3.
4. The probability of a randomly selected test having a score higher than 4 is 0.15.
- This is correct. It directly matches the calculated probability for a score greater than 4.
Thus, the correct interpretation of [tex]\( P(X > 4) \)[/tex] is:
The probability of a randomly selected test having a score higher than 4 is 0.15.
