In the statistic department of UCI, there are 60 graduate students in total, 45 PhD students and 15 master students. Among master students, 40% of them are international students. Among PhD students, 20% are international students. (a) What is the proportion of international students in the statistic department? (b) What is the proportion of master students among all domestic students.

(a) The proportion of international students in the statistic department is 25%.

(b) The proportion of master students among all domestic students is 20%.

Step-by-step 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%.

1.3

step-by-step explanation:

3x2=6   9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x