in a population of 1,000 students, 50 were asked by random sampling what their plans were after graduation…

in a population of 1,000 students, 50 were asked by random sampling what their plans were after graduation from high school. their responses are shown in the table. using proportional reasoning, make a prediction about how many students you would expect to have plans to attend college.\n\n| intention after graduation | number of students |\n| ---- | ---- |\n| college | 27 |\n| job | 13 |\n| military | 2 |\n| no plans | 8 |\n\n\\(\\frac{27}{50}=\\frac{x}{1000}\\)\n\\(27,000 = 50x\\)\nabout would have plans to attend college.

in a population of 1,000 students, 50 were asked by random sampling what their plans were after graduation from high school. their responses are shown in the table. using proportional reasoning, make a prediction about how many students you would expect to have plans to attend college.\n\n| intention after graduation | number of students |\n| ---- | ---- |\n| college | 27 |\n| job | 13 |\n| military | 2 |\n| no plans | 8 |\n\n\\(\\frac{27}{50}=\\frac{x}{1000}\\)\n\\(27,000 = 50x\\)\nabout would have plans to attend college.

Answer

Explanation:

Step1: Set up proportion

We set up the proportion $\frac{27}{50}=\frac{x}{1000}$ based on the sample - to - population ratio, where 27 out of 50 students in the sample plan to attend college and $x$ is the number of students in the population of 1000 who plan to attend college.

Step2: Cross - multiply

Cross - multiplying the proportion gives us $27\times1000 = 50x$, which simplifies to $27000=50x$.

Step3: Solve for $x$

Dividing both sides of the equation $27000 = 50x$ by 50, we get $x=\frac{27000}{50}=540$.

Answer:

540