Question

North Carolina State University posts the grade distributions for its courses online. Students in Statistics 101 in the Fall 2007 semester received 26% A's, 42% B's, 20% C's, 10% D's, and 2% F's. Choose a Statistics 101 student at random. To "choose at random" means to give every student the same chance to be chosen.

The student's grade on a four-point scale (with A = 4) is a discrete random variable X with this probability distribution:

Value of X 0 1 2 3 4
Probability 0.02 0.10 0.20 0.42 0.26

(a) What values of random variable X are represented by the event "the student got a grade better than C"? Write your answer as a comma-separated list.
(b) What is the probability of the event from part (a)?

Answer 1

The answers are (a) he values of random variable X are represented by the event "the student got a grade better than C" is B and A which is represented as: Therefore X will take two value 3,4 (b) the required probability required is 0.68 that the random values of variable X are denoted by the event "the student got a grade better than C"

Explanation:

From the information given,

The grade for the student's on the point of four scale (with A = 4) = F D C B A

The Value of X = 0, 1, 2, 3, 4

The Probability =0.02 , 0.10, 0.20 ,0.42 , 0.26

Now,

(a)The values of random variable X are represented by the event "the student got a grade better than C" is B and A which is represented as: Therefore X will take two value 3,4

As it is known that values of random variable X are denoted by the event "the student got a grade better than C is denoted as 2 by the four-point scale (with A = 4).

However X will take the values that the student got a grade better than C is 3 and 4 which evaluated A and B respectively.

(b) The required probability of the event from part (a) is,

Now,

P (X>2)

P(X=3) + P (X=4)

= 0.42 + 0.26

Therefore, the required probability required is 0.68 that the random values of variable X are denoted by the event "the student got a grade better than C"