SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam.

Question

SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II grade 75 Show all your work. Indicate clearly the methods you use, because you will be ded the correctness of your method as well as on the accuracy and completeness of your results and on explanations. 1. The graphical display below shows the proportions of male and female students in the undergraduate, master's, and doctoral programs at a particular university. These are the only three programs available at this university. 1.0 t 0.8 Male 0.6 Female 0.4 0.2 0.0 Undergraduate Master's Doctoral Program (a) What does the display reveal about the way the gender balance varies between the three programs

Explanation / Answer

a) This is a relative frequency chart , where the males and females together account for 1 and thier relative contributions are read from the shaded region

So in this case , undergraduate program is balanced with almost 50% males and 50% females of all the students who enrolled in the undergraduate program

while masters has a male female distribution of 60:40 , doctoral programm has a distribution of close to 70:30

b) Yes , as we see that the percentage distribution of males and females is close to 70:30. This means that for every 100 doctoral students , 70 are males and 30 are females .

c) we know that2 events are are mutually exclusive or disjoint if they cannot both be true (occur) at the same time. However there are certain doctoral students who are females as well. Hence both events " student enrolled in doctoral " and " females" are not mutually exclusive. There are certain students in the university who are females doctorals

d) we know that 2 events are independent when probability that one event occurs in no way affects the probability of the other event occurring and 2 events are dependent when the probability of one event occurring influences the likelihood of the other event.

Here the events are dependent. Suppose we randomly pick a doctoral student and finds out that its a male student in that case the probability of female student wouldnt change. However , if we pick a female doctoral student then the probability of selecting a female student from the university would change. Hence the events are dependent here.

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