some states now allow online gambling. as a marketing manager for a casino, you need to determine the…

Explanation:

Step1: Identify the confidence - level and margin of error

For a 99% confidence level, the z - score $z_{\alpha/2}=2.576$. The margin of error $E = 0.05$.

Step2: Use the formula for sample size when $p$ is unknown

The formula for sample size $n$ when the proportion $p$ is unknown is $n=\frac{z_{\alpha/2}^{2}\times0.25}{E^{2}}$. Substitute $z_{\alpha/2}=2.576$ and $E = 0.05$ into the formula: [ \begin{align*} n&=\frac{(2.576)^{2}\times0.25}{(0.05)^{2}}\ &=\frac{6.635776\times0.25}{0.0025}\ &=\frac{1.658944}{0.0025}\ & = 663.5776 \end{align*} ] Round up to the nearest integer, so $n = 664$.

Step3: Use the formula for sample size when $p$ is known

The formula for sample size $n$ when the proportion $p$ is known is $n=\frac{z_{\alpha/2}^{2}\times p(1 - p)}{E^{2}}$. Given $p = 0.17$, then $1-p=0.83$, $z_{\alpha/2}=2.576$ and $E = 0.05$. [ \begin{align*} n&=\frac{(2.576)^{2}\times0.17\times0.83}{(0.05)^{2}}\ &=\frac{6.635776\times0.1411}{0.0025}\ &=\frac{0.936308}{0.0025}\ &=374.5232 \end{align*} ] Round up to the nearest integer, so $n = 375$.

Answer:

a. 664 b. 375