A company sends out $1000$ invitation to customers to apply for a new credit card. Historical data tells us that the response rate is $20\%$. The company needs between 170 to 230 applications. What is the probability that this will occur? Do this with and without the continuous correction factor.
Is this the correct approach?
$n=1000$
$p=.2$
$np=200$
$s=\sqrt{.2\cdot.8\cdot 1000}=12.6491$
$\Phi\left(\frac{230-200}{12.6491}\right)-\Phi\left(\frac{170-200}{12.6491}\right)=0.982294$
$\Phi\left(\frac{230.5-200}{12.6491}\right)-\Phi\left(\frac{169.5-200}{12.6491}\right)=0.984101$