Final answer:
The 95% confidence interval for the population's average speed, rounded to one decimal place, is 21.3 m.p.h. to 24.1 m.p.h. This calculation is based on the given sample mean, standard deviation, sample size, and z-score for a 95% confidence level.
Step-by-step explanation:
To calculate the 95% confidence interval for the population's average speed, we use the formula for a confidence interval for the mean, which is given by:
\[\bar{x} \pm z\frac{\sigma}{\sqrt{n}}\]
- \(\bar{x}\) is the sample mean
- \(z\) is the z-score corresponding to the confidence level
- \(\sigma\) is the standard deviation
- \(n\) is the sample size
For this problem, we have:
- \(\bar{x} = 22.7\) m.p.h.
- \(\sigma = 3.63\) m.p.h.
- \(n = 25\)
The z-score for a 95% confidence interval is approximately 1.96. Plugging the values into the formula gives:
\[22.7 \pm 1.96\frac{3.63}{\sqrt{25}}\]
\[22.7 \pm 1.96\times 0.726\]
\[22.7 \pm 1.4236\]
Therefore, the 95% confidence interval for the population's average speed is:
\[21.2764 \text{ m.p.h.} \text{ to } 24.1236 \text{ m.p.h.}\]
Rounded to one decimal place, the confidence interval is \(21.3 m.p.h. to 24.1 m.p.h.\).