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The grade distribution for students in the 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.

\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}

What is the probability that a randomly selected student earned a C or better?

A. 0.17
B. 0.26
C. 0.48
D. 0.91


Sagot :

To find the probability that a randomly selected student earned a C or better, we need to consider the grades that correspond to C or better. According to the provided table:

- A grade of [tex]\(4\)[/tex] corresponds to an A.
- A grade of [tex]\(3\)[/tex] corresponds to a B.
- A grade of [tex]\(2\)[/tex] corresponds to a C.

We won't consider grades below C (i.e., 1 for D and 0 for F).

Now we need to find the probabilities of the grades that are C or better, which are 4, 3, and 2. According to the table, the probabilities are:

- The probability of getting an A (grade 4) is 0.43.
- The probability of getting a B (grade 3) is 0.31.
- The probability of getting a C (grade 2) is 0.17.

To find the total probability that a randomly selected student earned a C or better, we sum these probabilities up:

[tex]\[ \text{Probability (C or better)} = \text{Probability (A)} + \text{Probability (B)} + \text{Probability (C)} \][/tex]

Substituting the given probabilities:

[tex]\[ \text{Probability (C or better)} = 0.43 + 0.31 + 0.17 \][/tex]

Adding these values together:

[tex]\[ 0.43 + 0.31 + 0.17 = 0.91 \][/tex]

Thus, the probability that a randomly selected student earned a C or better is [tex]\(0.91\)[/tex].

So, the correct answer is [tex]\(\boxed{0.91}\)[/tex].
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