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The data you provided is a frequency distribution, and you are asking if it follows a normal distribution, with a significance level (α) of 5%.

### Given Data:
- Interval Classes: \(34 – 48, 49 – 63, 64 – 78, 79 – 93, 94 – 108, 109 – 123, 124 – 136\)
- Midpoints (\(X_i\)): \(41, 56, 71, 86, 101, 116, 130\)
- Frequencies (\(F_i\)): \(0, 0, 1, 31, 32, 3, 0\)
- Total Frequency (\(N\)): 67

### Steps to Test for Normality:
1. **Mean (\(\mu\))**: Calculate the mean of the data using weighted midpoints and frequencies.
   \[
   \mu = \frac{\sum (F_i \cdot X_i)}{N}
   \]
2. **Standard Deviation (\(\sigma\))**: Compute the standard deviation using:
   \[
   \sigma = \sqrt{\frac{\sum (F_i \cdot (X_i - \mu)^2)}{N}}
   \]
3. **Expected Normal Distribution**: For each interval, calculate the expected frequency based on the normal distribution:
   \[
   E_i = N \cdot P(X_i)
   \]
   where \(P(X_i)\) is the probability of the midpoint falling in each interval, calculated using the normal distribution function \(P(X_i) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(X_i - \mu)^2}{2\sigma^2}}\).
4. **Chi-Square Test**: Compare the observed frequencies with expected frequencies using the chi-square formula:
   \[
   \chi^2 = \sum \frac{(F_i - E_i)^2}{E_i}
   \]
5. **Conclusion**: Based on the chi-square statistic and the degrees of freedom (\(df = \text{number of classes} - 3\)), compare with the critical value from the chi-square table at \( \alpha = 0.05 \).

Would you like me to proceed with these calculations to test for normality?

### 5 Related Questions:
1. How do you interpret the chi-square test in hypothesis testing?
2. What are the assumptions of the chi-square goodness-of-fit test?
3. How is the normal distribution applied in real-world problems?
4. How do you calculate probabilities using the normal distribution curve?
5. What are the degrees of freedom in statistical tests, and why are they important?

**Tip**: The chi-square test works best with larger sample sizes, so ensure each class has a reasonable frequency for accurate results.

Apakah data di atas berdistribusi normal? α = 5%. Interval Kelas: 34 – 48, 49 – 63, 64 – 78, 79 – 93, 94 – 108, 109 – 123, 124 – 136. Nilai Tengah: 41, 56, 71, 86, 101, 116, 130. Frekuensi: 0, 0, 1, 31, 32, 3, 0. Jumlah Frekuensi: 67.

Test if a frequency distribution follows a normal distribution with a 5% significance level. The data includes class intervals (34-136), midpoints, and frequencies, using chi-square tests and normal distribution calculations. Ideal for advanced statistics students.

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