PLEASE ATTEMPT BOTH QUESTIONS FOR THUMBS UP Question 1 The Table below is taken

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PLEASE ATTEMPT BOTH QUESTIONS FOR THUMBS UP

Question 1

The Table below is taken from the Australian Government’s Department of Education and Training. It provides data on number of offers made to high school graduates for admission into Australian university programs in various fields of education (discipline). The data is taken from the website https://docs.education.gov.au/documents/undergraduate-applications-and-offers-february-2016. Students having the best academic grade in high school would be in the ATAR band 90.05 or more, and the worst in the band 50.00 or less.

a) Based on the proportion of offers made for different grades, which discipline is the most popular for the best students and what is that proportion?

b) If an Australian student is selected at random, then from the table above, what is the probability that he or she is studying “Society and Culture” and had an ATAR score of 80.00 or less?

c) Based on the proportion of offers made, which discipline has the highest proportion of students with the lowest ATAR grades, and what is that proportion?

d) Which discipline has majority of the students from “No ATAR/Non-Yr 12” background? Please find out the reasons for that through internet searches?

Table 11: Share of Year 12 offers by ATAR band for each field of education, February 2016 90.05 or No ATAR/ 8 2 50.00 or less 70.05- 80.00 80.05 0 60.00 70.00 3 Physical Sciences Engineering and Architecture and Environmental and Related Studies Management and Society and Culture Note: Hospitality and Mixed Field Programs are not shown due to the small number of offers, hence the total number of offers does not equal the sum of offers by broad field of education in the above

Explanation / Answer

a. Comparing rows of column 6 (ATAR band 90.5 or more), one can see that Engineering and related technologies is the most popular one with highest percentage and the proportion is 0.3 [30/100].

b. There are in total 46841 students studying society or culture and 40052 (9723+11610+18719) students have ATAR score of 80 or less. Thus, the probability of students studying society or culture is 46841/221060 [# of favourable outcomes/total outcomes], and probability of students have ATAR score of 80 or less is 40052/221060. Therefore, P(students studying society or culture AND students have ATAR score of 80 or less)=46841/221060*40052/221060=0.0384 [applying multiplication rule for disjoint events, P(A and B)=P(A)*P(B)]

c. By comparing rows of column 1 (50 or less), education is the most popular discipline among students with lowest ATAR grades and th eproportion is 0.073 [7.3/100].

d. Comparing number of students for different rows of column 7 (No ATAR/Non-Yr 12), health discipline has majority of the students (31,341). Most of the students who donot have ATAR ranking, end up taking a generalized course in science followed by shifting in their choicest discipline in the second year of their study. They get one good year for preparation which help them to secure position in the health discipline.

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