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

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

What is the probability that a randomly selected student got a B?

A. 0.17
B. 0.31
C. 0.43
D. 0.74



Answer :

GinnyAnswer
To determine the probability that a randomly selected student got a B, we need to understand that the sum of all probabilities should equal 1. The given probabilities for grades A, C, D, and F are 0.43, 0.17, 0.05, and 0.04 respectively. We'll use these values to find the missing probability for grade B.

Here is your step-by-step solution:

1. Identify the given probabilities:
- Probability of getting an A (grade 4) = 0.43
- Probability of getting a C (grade 2) = 0.17
- Probability of getting a D (grade 1) = 0.05
- Probability of getting an F (grade 0) = 0.04

2. Sum the given probabilities:
[tex]\[ 0.43 (A) + 0.17 (C) + 0.05 (D) + 0.04 (F) = 0.69 \][/tex]

3. Calculate the missing probability for grade B (grade 3):
Since the total probability must equal 1, subtract the sum of the given probabilities from 1:
[tex]\[ 1 - 0.69 = 0.31 \][/tex]

Therefore, the probability that a randomly selected student got a B is [tex]\( \boxed{0.31} \)[/tex].

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