Question

Questions 4- 7 refer to the following. Our Eco 320 course consists of sophomores and juniors. Ten percent of the students who take Econ 320 fail the course. Among those students who pass, 25 % are sophomores. 7.5% of the students are juniors who failed the class. Of those who pass, 20 % will receive an A for the course. What is the probability that a randomly selected student will be a junior? (10 points) 4. 225 25 .675 70 75 a. b. d. e. 5. If a student is a sophomore, what is the probability that he/she will pass the class? (10 points) 12 32 a 38 40 90 d 6 Show whether the events "being a so phom ore" and "passing the course" are statis tically independent. (10 points) 7 What is the probability that a student will not make an A? (10 points)

Answer 1

(4)

From the given data, the following Table is calculated:

	Pass	Fail	Total
Sophomore	0.90 X 0.25 = 0.225	0.025	0.25
Junior	0.90 - 0.225 = 0.675	0.075	0.75
Total	1 - 0.10 = 0.90	0.10	1.00

P(Junior) = 0.75

So,

Correct option:

e.   .75

(5)
P(Pass/ Sophomore) = P(Pass AND Sophomore)/P(Sophomore)

                              = 0.225/ 0.25

                              = 0.90

So,

Correct option:

e.    0.90

(6)

P(Sophomore) = 0.25

P(Pass) = 0.90

P(Sophomore) X P(Pass) = 0.25 X 0.90 = 0.225

P(Sophomore AND Pass) = 0.225

Since P(Sophomore AND Pass) = P(Sophomore) X P(Pass) , the events: "being sophomore" and "passing the course" are independent.

(7)

P(Will not make an A) = 0.90 X 0.80 = 0.72

So,

Answer is:

0.72