7 (Chapter 7 Section 7.2)
Question 7, 7.2.25-T
HW Score: $68.57 \%, 4.8$ of 7 points
Part 1 of 3
Points: 0 of 1
Refer to the accompanying data set and construct a $95 \%$ confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results. Click the icon to view the pulse rates for adult females and adult males.

Construct a $95 \%$ confidence interval of the mean pulse rate for adult fermales.
$\mathrm{bpm}< \mu< \square \mathrm{bpm}$
(Round to one decimal place as needed.)

Step 1 ：Given that the sample mean pulse rate for adult females is 70 bpm, the sample standard deviation is 10 bpm, and the sample size is 100.

Step 2 ：We are asked to construct a 95% confidence interval for the mean pulse rate. The formula for the confidence interval for a population mean is \(\bar{x} \pm Z_{\frac{\alpha}{2}} \frac{s}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(Z_{\frac{\alpha}{2}}\) is the Z-score corresponding to the desired confidence level (for a 95% confidence level, \(Z_{\frac{\alpha}{2}} = 1.96\)), \(s\) is the sample standard deviation, and \(n\) is the sample size.

Step 3 ：Substituting the given values into the formula, we get \(70 \pm 1.96 \frac{10}{\sqrt{100}}\).

Step 4 ：Solving the above expression, we get the lower limit as 68.0 bpm and the upper limit as 72.0 bpm.

Step 5 ：Thus, the 95% confidence interval of the mean pulse rate for adult females is \(\boxed{68.0 \, \text{bpm} < \mu < 72.0 \, \text{bpm}}\).