From a random sample of 81 dates, the mean record high daily temperature in a certain city has a mean of $84.55^{\circ} \mathrm{F}$. Assume the population standard deviation is $14.69^{\circ} \mathrm{F}$. This creates a $95 \%$ confidence interval for the population mean of $(81.35,87.75)$. Does it seem possible that the population mean could be greater than $89^{\circ} \mathrm{F}$ ? Explain.
Choose the correct answer below.
A. Yes, it seems possible because $89^{\circ} \mathrm{F}$ is between the endpoints of the confidence interval
B. No, it does not seem possible because $89^{\circ} \mathrm{F}$ is greater than the right endpoint of the confidence interval.
C. No, it does not seem possible because $89^{\circ} \mathrm{F}$ is less than the left endpoint of the confidence interval.
D. Yes, it seems possible because $89^{\circ} \mathrm{F}$ is greater than the right endpoint of the confidence interval.
Answer
\(\boxed{\text{The correct answer is B. No, it does not seem possible because } 89^{\circ} \mathrm{F} \text{ is greater than the right endpoint of the confidence interval.}}\)
Step 1 ：From a random sample of 81 dates, the mean record high daily temperature in a certain city has a mean of $84.55^{\circ} \mathrm{F}$. Assume the population standard deviation is $14.69^{\circ} \mathrm{F}$. This creates a $95 \%$ confidence interval for the population mean of $(81.35,87.75)$.
Step 2 ：Does it seem possible that the population mean could be greater than $89^{\circ} \mathrm{F}$ ?
Step 3 ：The correct answer is B. No, it does not seem possible because $89^{\circ} \mathrm{F}$ is greater than the right endpoint of the confidence interval.
Step 4 ：\(\boxed{\text{The correct answer is B. No, it does not seem possible because } 89^{\circ} \mathrm{F} \text{ is greater than the right endpoint of the confidence interval.}}\)
