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The grade distribution for students in an introductory statistics class at a local community college is displayed in the table below. Let [tex]\( X \)[/tex] represent the grade for a randomly selected student.

| Grade | 4 | 3 | 2 | 1 | 0 |
|-------------|-----|-----|-----|-----|-----|
| Probability | 0.43| 0.31| 0.17| 0.05| 0.04|

Which of the following correctly represents the probability that a randomly selected student has a grade higher than a C?

A. [tex]\( P(X \ \textless \ 2) \)[/tex]
B. [tex]\( P(X \leq 2) \)[/tex]
C. [tex]\( P(X \ \textgreater \ 2) \)[/tex]
D. [tex]\( P(X \geq 2) \)[/tex]

Sagot :

GinnyAnsweridn
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].
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