holiday presents how large a sample is needed to estimate the population mean for the amount of money a…

Explanation:

Step1: Identify the formula

The formula for sample - size $n$ when estimating the population mean is $n=\left(\frac{z_{\alpha/2}\sigma}{E}\right)^2$, where $z_{\alpha/2}$ is the z - value corresponding to the level of confidence, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 95% confidence interval, the significance level $\alpha = 1-0.95 = 0.05$, and $\alpha/2=0.025$. The $z$ - value $z_{\alpha/2}=z_{0.025}=1.96$. The population standard deviation $\sigma = 9.50$ and the margin of error $E = 2$.

Step2: Substitute the values into the formula

Substitute $z_{\alpha/2}=1.96$, $\sigma = 9.50$, and $E = 2$ into the formula $n=\left(\frac{z_{\alpha/2}\sigma}{E}\right)^2$. $n=\left(\frac{1.96\times9.50}{2}\right)^2$. First, calculate $\frac{1.96\times9.50}{2}$: $1.96\times9.50 = 18.62$, and $\frac{18.62}{2}=9.31$. Then, $n=(9.31)^2=86.6761$.

Step3: Round up the result

Since the sample - size $n$ must be a whole number, and we want to be at least 95% confident with a margin of error of $2$, we round up $86.6761$ to the next whole number.

Answer:

87