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. which of the following correctly represents the probability that a randomly selected student has a grade higher than a c? ( p(x < 2) ) ( p(x leq 2) ) ( p(x > 2) ) ( p(x geq 2) )

Explanation:

Step1: Analyze grade - value mapping

Given \(A = 4\), \(B=3\), \(C = 2\). A grade higher than \(C\) means \(A\) or \(B\). So the values of \(X\) for grades higher than \(C\) are \(X = 3\) (for \(B\)) and \(X = 4\) (for \(A\)).

Step2: Translate to probability notation

The probability that \(X\) takes a value greater than \(2\) (\(P(X>2)\)) represents the probability that the grade is \(B\) (\(X = 3\)) or \(A\) (\(X = 4\)) since \(X\) is a discrete random variable with values \(0,1,2,3,4\).

Answer:

\(P(X > 2)\)