Question

There are 8,253 men and 10,327 women at a state university. If 43% of the men are in business and 27% of the women are in business majors. What is the expected number of majors in a random sample of 200 students?

Answer 1

To find the expected number of business majors in a random sample of 200 students, we need to calculate the proportion of business majors in each gender group and multiply it by the size of the respective group.

Step-by-step explanation:

To find the expected number of business majors in a random sample of 200 students, we need to calculate the proportion of business majors in each gender group and multiply it by the size of the respective group.

For the men, the proportion of business majors is 43%, so the expected number of business majors among them is 0.43 * 8,253 = 3,548.

For the women, the proportion of business majors is 27%, so the expected number of business majors among them is 0.27 * 10,327 = 2,794.

Adding the expected number of business majors from both genders, we get 3,548 + 2,794 = 6,342.

Therefore, the expected number of business majors in a random sample of 200 students is 6,342.

Answer 2

68 students

Step-by-step explanation:

Number of men who major in business in the university= 0.43*8253=3548.79

Rounding off we have 3549 students

Number of women who major in business in the university= 0.27*10327=2788.29

Approximately 2789 students

Total students who major in Business= 3549+2789=6338 students

Total students in school= 8253+10327=18580

Probability of getting business major= 6338/18580

Out of 200 students, we expect

`\frac {6338}{18580} * 200=68.22389666`

Approximately 68 students will be majoring in business