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	326	197	251	774
	Part-Time	150	161	194	505
	Totals	476	358	445	1,279

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.

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Answer 1

a)

dividing each value with total of 1279:

	Business	Engg	Other	Total
full time	0.2549	0.1540	0.1962	0.6052
part time	0.1173	0.1259	0.1517	0.3948
Total	0.3722	0.2799	0.3479	1.0000

b)

P(B) =0.3722 ; P(E) =0.2799 ; P(O) =0.3479

so business is the undergraduate major that produces the most potential MBA students.

c)

P(Engineering major|full time)=197/774=

0.2545

d)

P(full time|business)=326/476=

0.6849

e)

No

since P(full time|business) not equal to P(full time) , therefore event F and B are nt independent