Answer:
Option C) 1537
Explanation:
We are given the following in the question:
Population standard deviation = $5000
95% confidence interval width = $500
Thus, margin of error = $250
Formula for margin of error =
[tex]z_{stat}\times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]250 = 1.96\times \dfrac{5000}{\sqrt{n}}\\\\n = (1.96\times \dfrac{5000}{250})^2\\\\n = 1536.64\\n \approx 1537[/tex]
Thus, the correct answer is
Option C) 1537
