Question

North Carolina State University posts the grade distributions for its courses online.$3$Students in Statistics $101$in a recent semester received $26\%$As, $42\%$Bs, $20\%$Cs, $10\%$Ds, and $2\%$Fs. Choose a Statistics $101$student at random. The student’s grade on a four-point scale (with $A=4$) is a discrete random variable X with this probability distribution:

Say in words what the meaning of$P(X\ge 3)$ is. What is this probability?

Short answer

$P(X\ge 3)$represents the probability that student will get a $\mathrm{B}$or more.

The required probability is $0.819$.

Step-by-step solution

Given information 

Given in the question that, the North Carolina State University posts the grade distributions for its courses online.3 Students in Statistics 101 in a recent semester received $26\%$As, $42\%$Bs, $20\%$Cs, $10\%$Ds, and$2\%$Fs. Choose a Statistics $101$student at random. The student’s grade on a four-point scale (with A = $4$) is a discrete random variable $X$with this probability distribution:

Explanation

The table is:

Value	$0$	$1$	$2$	$3$	$4$
Probability	$0.011$	$0.032$	?	$.362$	$0.457$

To explain the term, the missing value is required to be computed. Let the missing value be $x$. The missing value can be calculated as:

localid="1649851625209" $0.011+0.032+x+0.362+0.457=1$

$x+0.862=1$

$x=0.138$

$P(X\ge 3)$can be calculated as:

localid="1649918332279" $$\begin{gathered} P(X\ge 3)=P(X=3)+P(X=4) \\ =0.362+0.457 \\ =0.819 \end{gathered}$$