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The grade distribution for students in an introductory statistics class at a local community college is displayed in the table. In this table, [tex]\( A=4, B=3, \)[/tex] etc. Let [tex]\( X \)[/tex] represent the grade for a randomly selected student.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Grade & 4 & 3 & 2 & 1 & 0 \\
\hline
Probability & 0.43 & 0.31 & 0.17 & 0.05 & 0.04 \\
\hline
\end{tabular}
\][/tex]

Which of the following correctly represents the probability that a randomly selected student has a grade higher than [tex]\( C \)[/tex]?

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 :

GinnyAnswer
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.
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