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 MajorBusiness Engineering Other TotalsFull-Time 352 197 251 800Part-Time 150 161 194 505Totals 502 358 445 1,305
If required, round your answers to four decimal places.
(a) Develop a joint probability table for these data.
(b) Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major 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?(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?

a) The joint probability table is

U | Busine | Engin | Others | Total

F | 0.2697 | 0.1510 | 0.1923 | 0.6130

Pa | 0.1149 | 0.1234 | 0.1487 | 0.3870

T | 0.3846 | 0.2744 | 0.3410 | 1.0000

b) From the joint probability table, the business undergraduate major has the highest total probability (0.3846) and therefore, produces the most potential MBA students

c) P(Engineering | Full time) = 0.2463

d) P(Full time | Business) = 0.7012

Step-by-step explanation:

U | Busi | Eng | Oth | Totals

Fu | 352 | 197 | 251 | 800

Pa | 150 | 161 | 194 | 505

T | 502 | 358 | 445 | 1,305

a) To develop the joint probability table, we first take note that the total population = 1305.

To find the joint probability of each categories sub-category, we divide each cell in the table by the total population.

The table becomes

U | Busine | Engin | Others | Total

F | 0.2697 | 0.1510 | 0.1923 | 0.6130

Pa | 0.1149 | 0.1234 | 0.1487 | 0.3870

T | 0.3846 | 0.2744 | 0.3410 | 1.000

b) From the joint probability table, the business undergraduate major has the highest total probability (0.3846) and hence, produces the most potential MBA students.

c) P(Eng|F) = P(Eng n F)/P(F)

Reading the probabilities from the tables.

P(Eng|F) = (0.1510/0.613) = 0.2463

d)

P(Full-time | Business) = P(F n Bus)/P(Bus)

From the tables

P(Full-time | Business) = (0.2697/0.3846) = 0.7012

Hope this Helps!!!

1

step-by-step explanation:

it's the only multiple of both and the least