A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Chevrolet Aveo. A random sample of 5 cars had a mean time on the dealer's lot of 54 days. Assume the population standard deviation t 6 days. Find the best point estimate of the population mean and the 95% confidence interval of the population mean.

Step 1:

Organize the given information

\[n=50\]

\[\overline{x}=54\]

\[\sigma=6\]

\[C=95\%\]

Step 2:

Find the \(Z_{\frac{\alpha}{2}}\) value by either using the z-table or the quick chart.

\[Z_{\frac{\alpha}{2}}=1.96\]

Step 3: 

Plug into our formula

\[\overline{x}-Z_{\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt{n}}\leq \mu\leq \overline{x}+Z_{\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt{n}} \]

\[54-(1.96)\cdot\left(\frac{6}{\sqrt{50}}\right)\leq\mu\leq 54+(1.96)\cdot\left(\frac{6}{\sqrt{50}}\right) \]

\[52.3\leq\mu\leq 55.7\]