The McClellan Development Authority $($a non$-$profit commercial development agency$)$ wishes to test its belief that $35\%$ of business owners nationwide recognize the advantages of re$-$locating to Calhoun County. The Authority wants to be $99\%$ confident in its study's results, only wants a range of error up to $1\mathrm{.}5\%,$ and estimates the standard deviation to be $3\mathrm{.}77.$ What minimum sample size is required?

Formulae You Might Need:

$n=(Z\frac{S}{E}{)}^2$

$n=\frac{Z^{2}pq}{E^2}$