1. **Problem Statement:** Professor Linda wants to determine the sample size for a population of 275 BAM students with a margin of error of 1%. 2. **Formula Used:** The sample size $n$ for a finite population can be calculated using the formula: $$n = \frac{N \times Z^2 \times p \times (1-p)}{E^2 \times (N-1) + Z^2 \times p \times (1-p)}$$ where: - $N$ = population size - $Z$ = Z-value (standard score) corresponding to the confidence level - $p$ = estimated proportion of an attribute present in the population (if unknown, use 0.5 for maximum variability) - $E$ = margin of error (as a decimal) 3. **Important Rules:** - For a 99% confidence level (since margin of error is 1%), $Z \approx 2.576$. - Use $p=0.5$ if no prior estimate is available. - Convert margin of error percentage to decimal: $1\% = 0.01$. 4. **Substitute values:** - $N = 275$ - $Z = 2.576$ - $p = 0.5$ - $E = 0.01$ 5. **Calculate numerator:** $$275 \times (2.576)^2 \times 0.5 \times 0.5 = 275 \times 6.635 \times 0.25 = 275 \times 1.65875 = 456.15625$$ 6. **Calculate denominator:** $$0.01^2 \times (275 - 1) + (2.576)^2 \times 0.5 \times 0.5 = 0.0001 \times 274 + 6.635 \times 0.25 = 0.0274 + 1.65875 = 1.68615$$ 7. **Calculate sample size:** $$n = \frac{456.15625}{1.68615} \approx 270.56$$ 8. **Interpretation:** Since sample size cannot exceed population, and $n \approx 271$ is close to population size 275, the sample size is 271. **Final answer:** The sample size Professor Linda should take is **271** students.