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To determine the probability that a randomly selected student has a grade higher than [tex]\( C \)[/tex], we need to identify the grades that fall into this category. In the grade scale provided, [tex]\( A \)[/tex] is 4, [tex]\( B \)[/tex] is 3, [tex]\( C \)[/tex] is 2, [tex]\( D \)[/tex] is 1, and [tex]\( F \)[/tex] is 0.
A grade higher than [tex]\( C \)[/tex] would refer to grades [tex]\( A \)[/tex] (4) and [tex]\( B \)[/tex] (3). So, we are looking for [tex]\( P(X > 2) \)[/tex].
The probabilities associated with each grade are given as:
- Grade 4: Probability = 0.43
- Grade 3: Probability = 0.31
- Grade 2: Probability = 0.17
- Grade 1: Probability = 0.05
- Grade 0: Probability = 0.04
To find [tex]\( P(X > 2) \)[/tex], we need to sum the probabilities of grades 4 and 3:
[tex]\[ P(X > 2) = P(X = 4) + P(X = 3) \][/tex]
Substituting the given probabilities:
[tex]\[ P(X > 2) = 0.43 + 0.31 = 0.74 \][/tex]
Therefore, the correct representation of the probability that a randomly selected student has a grade higher than [tex]\( C \)[/tex] is [tex]\( P(X > 2) \)[/tex] with a calculated probability of 0.74.
A grade higher than [tex]\( C \)[/tex] would refer to grades [tex]\( A \)[/tex] (4) and [tex]\( B \)[/tex] (3). So, we are looking for [tex]\( P(X > 2) \)[/tex].
The probabilities associated with each grade are given as:
- Grade 4: Probability = 0.43
- Grade 3: Probability = 0.31
- Grade 2: Probability = 0.17
- Grade 1: Probability = 0.05
- Grade 0: Probability = 0.04
To find [tex]\( P(X > 2) \)[/tex], we need to sum the probabilities of grades 4 and 3:
[tex]\[ P(X > 2) = P(X = 4) + P(X = 3) \][/tex]
Substituting the given probabilities:
[tex]\[ P(X > 2) = 0.43 + 0.31 = 0.74 \][/tex]
Therefore, the correct representation of the probability that a randomly selected student has a grade higher than [tex]\( C \)[/tex] is [tex]\( P(X > 2) \)[/tex] with a calculated probability of 0.74.
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