Northwood High has a total student population of 1,500, and Southwood High has a total student population of 1,800. Bas…

The correct answer is 1,125.

First, determine the proportion of students who prefer Email and Text Message at each school based on the survey data. These proportions will be used to project the numbers for the entire school populations.

For Northwood High (200 students sampled):

- Proportion preferring Email: 50/200 = 0.25

- Proportion preferring Text Message: 100/200 = 0.50

For Southwood High (300 students sampled):

- Proportion preferring Email: 60/300 = 0.20

- Proportion preferring Text Message: 200/300 = 2/3

Next, project the initial number of students for each preference at each school using their total populations.

For Northwood High (1,500 total students):

- Initial projected Email: 0.25 · 1,500 = 375

- Initial projected Text Message: 0.50 · 1,500 = 750

For Southwood High (1,800 total students):

- Initial projected Email: 0.20 · 1,800 = 360

- Initial projected Text Message: (2/3) · 1,800 = 1,200

Now, calculate the number of students who switch from Text Message to Email at each school.

- Northwood switchers: 20% of 750 = 0.20 · 750 = 150

- Southwood switchers: 20% of 1,200 = 0.20 · 1,200 = 240

Finally, calculate the new total number of students preferring Email at each school and then sum them.

- New Northwood Email total: 375 (initial) + 150 (switchers) = 525

- New Southwood Email total: 360 (initial) + 240 (switchers) = 600

- Combined total: 525 + 600 = 1,125

A is incorrect because it is the result of performing the calculation on the raw survey numbers without projecting to the full student populations (initial survey Email total of 110 plus 20% of the initial survey Text total of 300, which is 110 + 60 = 170). B is incorrect because it is the initial projected number of students who prefer Email (375 + 360 = 735), before accounting for the students who switch their preference. C is incorrect because it is the result of incorrectly pooling the survey data from both schools (110/500 for Email, 300/500 for Text) and applying these single proportions to the total population of 3,300, which fails to account for the different preferences at each school.