Answer:
[tex]n\geq 2400[/tex]
Step-by-step explanation:
-The standard deviation of the estimated proportion that is less than or equal to 1% is calculated as follows:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\leq 0.01\\\\\\\\\sqrt{\frac{0.4\times0.6}{n}}\leq 0.01[/tex]
#We take square root on both sides:
[tex]\frac{0.4\times0.6}{n}\leq 0.01^2\\\\\\n\geq {\frac{0.4\times0.6}{0.01^2}\\\\n\geq 2400[/tex]
Hence, the sample size must at least 2400
