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The problem in the image asks to determine a 95% confidence interval for the average annual distance traveled by cars in Province A. Here's the information given:

- Sample size (\( n \)): 100 cars
- Sample mean (\( \bar{x} \)): 23,500 km/year
- Standard deviation (\( s \)): 3,900 km
- Confidence level: 95%

We can calculate the confidence interval using the formula for the confidence interval of the mean:

\[
CI = \bar{x} \pm z_{\alpha/2} \times \frac{s}{\sqrt{n}}
\]

Where:
- \( \bar{x} \) is the sample mean (23,500 km/year),
- \( s \) is the standard deviation (3,900 km),
- \( n \) is the sample size (100),
- \( z_{\alpha/2} \) is the z-value corresponding to a 95% confidence level (for 95%, \( z_{\alpha/2} \approx 1.96 \)).

Let me compute the confidence interval.The 95% confidence interval for the average annual distance traveled by cars in Province A is approximately between **22,735.6 km** and **24,264.4 km**.

Let me know if you'd like more details or if you have any other questions. Here are five related questions to explore further:

1. How does increasing the sample size affect the width of the confidence interval?
2. What is the difference between a 95% and 99% confidence interval?
3. How would the confidence interval change if the standard deviation were smaller?
4. How do you calculate the z-value for different confidence levels?
5. What assumptions are necessary for using this confidence interval formula?

**Tip:** A narrower confidence interval can be achieved by increasing the sample size or reducing the variability (standard deviation) in the data.

Berdasarkan sample 100 mobil di provinsi A menunjukkan bahwa rataan jarak tempuh sebesar 23,500 km/tahun dengan simpangan baku 3900 km. Selang kepercayaan 95% bagi rataan jarak tempuh mobil per tahun di provinsi tersebut adalah berapa?

Pelajari cara menentukan selang kepercayaan 95% untuk rataan jarak tempuh mobil di Provinsi A, menggunakan simpangan baku 3900 km dan rata-rata 23,500 km/tahun. Contoh soal ini melibatkan konsep statistik seperti selang kepercayaan, distribusi normal, dan teorema limit pusat. Cocok untuk siswa tingkat SMA.

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