Question

the grade distribution for students in the introductory statistics class at a local community college are displayed in the table. in this table, a = 4, b = 3, etc. let x represent the grade for a randomly selected student. what is the probability that a randomly selected student got a b? 0.17 0.31 0.43 0.74

Explanation:

Step1: Recall the property of probability distribution

The sum of all probabilities in a probability distribution is \(1\).
Let \(P(X = 3)\) be the probability of getting a \(B\).
We know that \(\sum_{i}P(X=x_i)=1\), where \(x_i\) are the grade values (\(4,3,2,1,0\)) and \(P(X = x_i)\) are their corresponding probabilities.

Step2: Set up the equation

\(P(X = 4)+P(X = 3)+P(X = 2)+P(X = 1)+P(X = 0)=1\)
Substitute the known values: \(0.43 + P(X = 3)+0.17+0.05 + 0.04=1\)

Step3: Simplify the left - hand side of the equation

First, add the known probabilities: \(0.43+0.17+0.05 + 0.04=\frac{43 + 17+5 + 4}{100}=\frac{69}{100}=0.69\)
The equation becomes \(0.69+P(X = 3)=1\)

Step4: Solve for \(P(X = 3)\)

Subtract \(0.69\) from both sides of the equation: \(P(X = 3)=1 - 0.69\)
\(P(X = 3)=0.31\)

Answer:

\(0.31\) (the second option)