Question

Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.

		Undergraduate Major
		Business	Engineering	Other	Totals
Intended Enrollment Status	Full-Time	350	197	251	798
	Part-Time	150	161	194	505
	Totals	500	358	445	1,303

If required, round your answers to four decimal places.

(a)

Develop a joint probability table for these data.

		Undergraduate Major
		Business	Engineering	Other	Totals
Intended Enrollment Status	Full-Time
	Part-Time
	Totals

(b)

Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students.

P(B) =  , P(E) =  , and P(O) =  , so business is the undergraduate major that produces the most potential MBA students.

(c)

If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major?

P (Engineering | Full-Time) =

(d)

If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree?

P (Full-Time | Business) =

(e)

Let F denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate business major. Are events F and B independent?

- Select your answer -YesNoItem 18

Justify your answer.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

a) below is  joint probability table after dividing each cell with 1303:

	Business	Engineering	Other	Totals
Full-Time	0.2686	0.1512	0.1926	0.6124
Part-Time	0.1151	0.1236	0.1489	0.3876
Totals	0.3837	0.2748	0.3415	1.0000

b)

P(B)=0.3837 , P(E)=0.2748 , P(O)= 0.3415 , so business is the undergraduate major that produces the most potential MBA students.

c)

P (Engineering | Full-Time) = 197/798 =0.2469

d)

P (Full-Time | Business) =350/500 =0.7000

e)

no , as P(Full-Time | Business) is not equal to P(full time)