Answer:
(a) The proportion of international students in the statistic department is 25%.
(b) The proportion of master students among all domestic students is 20%.
Explanation:
The following can first be obtained from the question:
Total number of graduate students = 60
Number of PhD students = 45
Number of Master students = 15
Percentage of international students among the master students = 40%
Percentage of international students among the PhD students = 20%
Number of international master students = Number of Master students * Percentage of international students among the master students = 15 * 40% = 6
Number of international PhD students = Number of PhD students * Percentage of international students among the PhD students = 45 * 20% = 9
The questions can now be answered as follows:
(a) What is the proportion of international students in the statistic department?
This can be calculated as follows:
Total number of international students = Number of international master students + Number of international PhD students = 6 + 9 = 15
Total number of graduate students = 60
Proportion of international students in the statistic department = Total number of international students / Total number of graduate students = 15 / 60 = 0.25, or 25%
Therefore, the proportion of international students in the statistic department is 25%.
(b) What is the proportion of master students among all domestic students.
This can be calculated as follows:
Total number of graduate students = 60
Total number of international students = Number of international master students + Number of international PhD students = 6 + 9 = 15
Total number of domestic students = Total number of graduate students - Total number of international students = 60 - 15 = 45
Number of Master students = 15
Number of international master students = Number of Master students * Percentage of international students among the master students = 15 * 40% = 6
Number of domestic master students = Number of Master students - Number of international master students = 15 - 6 = 9
Proportion of master students among all domestic students = Number of domestic master students / Total number of domestic students = 9 / 45 = 0.20, or 20%
Therefore, the proportion of master students among all domestic students is 20%.