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



Answer :

To determine the probability that a randomly selected student earned a grade of C or better, we need to sum the probabilities of receiving grades A, B, and C. These grades correspond to the numerical values 4, 3, and 2, respectively.

Given the probabilities:
- Probability of getting an A (4): [tex]\(0.43\)[/tex]
- Probability of getting a B (3): [tex]\(0.31\)[/tex]
- Probability of getting a C (2): [tex]\(0.17\)[/tex]

We sum these probabilities to find the probability of earning a C or better:

[tex]\[ \text{Probability of earning a C or better} = \text{Probability of A} + \text{Probability of B} + \text{Probability of C} \][/tex]

[tex]\[ \text{Probability of earning a C or better} = 0.43 + 0.31 + 0.17 \][/tex]

Adding these values together:

[tex]\[ 0.43 + 0.31 = 0.74 \][/tex]

[tex]\[ 0.74 + 0.17 = 0.91 \][/tex]

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

The correct answer is:
[tex]\[ \boxed{0.91} \][/tex]

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