To determine which statement correctly represents the probability that a randomly selected student has a grade higher than a C, we need to understand the grading scale provided:
- A is represented by 4.
- B is represented by 3.
- C is represented by 2.
- D is represented by 1.
- F is represented by 0.
Grades higher than a C would be grades A and B. Therefore, we wish to calculate the probability that a randomly selected student has a grade of either A or B.
The probabilities given in the table are:
- Probability of A (4) = 0.43
- Probability of B (3) = 0.31
- Probability of C (2) = 0.17
- Probability of D (1) = 0.05
- Probability of F (0) = 0.04
To find the probability that a student has a grade higher than a C, we need to add the probabilities of getting an A or a B:
[tex]\[ P(X > 2) = P(\text{A}) + P(\text{B}) \][/tex]
[tex]\[ P(X > 2) = 0.43 + 0.31 \][/tex]
[tex]\[ P(X > 2) = 0.74 \][/tex]
Therefore, the correct statement representing the probability that a randomly selected student has a grade higher than a C is [tex]\( P(X > 2) \)[/tex].
