4. GMAC MBA NEW-MARTICULANTS SURVEY MBA programs in various colleges and univers
ID: 3061231 • Letter: 4
Question
4. GMAC MBA NEW-MARTICULANTS SURVEY
MBA programs in various colleges and universities in the United States often administer the Graduate Management Admissions Council (GMAC) MBA New-Matriculants Survey to their new students each year. Data collected on two types of information typically received the most attention from these various MBA programs: the age group of the new matriculants and whether or not they applied to more than one school. Recently this survey provided the following data.
Age
Group
Applied to More Than One School
Yes
No
23 and under
207
201
24-26
299
379
27-30
185
268
31-35
66
193
36 and over
51
169
Suppose you are a decision maker in an MBA program. Provide answers to the following questions.
What is the probability that a randomly selected MBA applicant would be 23 years of age or younger?
What is the probability that a randomly selected MBA applicant would be older than 26?
What is the probability that a randomly selected MBA applicant would apply to more than one school?
If a randomly selected MBA applicant applied to more than one school, what is the probability that such an applicant is between the ages of 24 and 26?
If a randomly selected MBA applicant is at least 36 years of age, what is the probability that such an applicant applied to more than one school?
What is the probability that a randomly selected MBA applicant is between the ages of 24 and 26 or applied to more than one school?
Suppose that a randomly selected MBA applicant has applied to only one school. What is the probability that such an applicant is at least 31 years of age?
Does it appear as though the number of schools applied to MBA applicants is independent of age? Explain.
Age
Group
Applied to More Than One School
Yes
No
23 and under
207
201
24-26
299
379
27-30
185
268
31-35
66
193
36 and over
51
169
Explanation / Answer
The sumamry table is shown below:
Probability that a randomly selected MBA applicant would be 23 years of age or younger = 408/2018 = 0.2022
Probability that a randomly selected MBA applicant would be older than 26= (453+259+220) / 2018 = 932/2018 = 0.4618
Probability that a randomly selected MBA applicant would apply to more than one school = 808/2018 = 0.4004
No.of applicants applied to more than one school = 808
Out of these, applicants aged between 24 and 26 = 299
So, the probability that an applicant is aged between 24 and 26, provided he has applied to more than one school = 299/808 = 0.37
No. of applicants at least 36 years of age = 220
The probability that such an applicant at least 36 years of age applied to more than one school = 51/220 = 0.2318
The probability that a randomly selected MBA applicant is between the ages of 24 and 26 or applied to more than one school = ((299+379) + 808 - 299)/2018 = (379+808)/2018 = 0.5882
No.of students applied to only one school = 1210
The probability that an applicant is at least 31 years of age, provided he has not applied to more than one school = (193+169)/1210 = 362/1210 = 0.2992
Does it appear as though the number of schools applied to MBA applicants is independent of age: NO.
We see that more number of students in the age group 23 and under apply to more than one schools, but for other age groups, number of students applying to more than one schools is lower than the number of students applying to one school.
Also, we see that the difference between the number of students applying to one school and multiple schools goes on increasing with age.
So we can conclude that the two events: number of schools applied to and age, are not independent.
Yes No Total 23 and under 207 201 408 24-26 299 379 678 27-30 185 268 453 31-35 66 193 259 36 and over 51 169 220 Total 808 1210 2018Related Questions
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