Answer: 1537.
Step-by-step explanation:
Formula for sample size :-
[tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2[/tex]
Given : [tex]\sigma=2000[/tex]
Margin of error : E= 100
Critical value of 95% confidence : [tex]z_{\alpha/2}=1.96[/tex]
Now, the required sample size will be :-
[tex]n=(\dfrac{1.96\cdot 2000}{100})^2\\\\=1536.64\approx1537[/tex]
Hence, the minimum sample size required = 1537.