ANSWER:
2333 students
STEP-BY-STEP EXPLANATION:
Given:
Margin of error (E): 4
Standard deviation (σ): 75
Confidence level (CI): 99%
For this confidence level the value of z is equal to 2.576.
We can calculate the necessary sample size with the following formula:
[tex]E=z\cdot\left(\frac{\sigma}{\sqrt{n}}\right)[/tex]Substituting each value we calculate the value of n, like this:
[tex]\begin{gathered} 4=2.576\cdot \left(\frac{75}{\sqrt{n}}\right) \\ \\ \frac{75}{\sqrt{n}}=\frac{4}{2.576} \\ \\ \sqrt{n}=\frac{75\cdot2.576}{4} \\ \\ n=\left(\frac{75\cdot2.576}{4}\right)^2 \\ \\ n=2332.89\cong2333 \end{gathered}[/tex]The number of students to be selected must be 2333
