To determine if the frequency distribution appears to be a normal distribution, we need to construct the frequency distribution table based on the given earthquake magnitudes. However, since the actual earthquake magnitudes are not provided in the question, I will guide you on how to construct the table and assess normality.
Determine Class Intervals:
- Start with a lower class limit of 1.0.
- Decide on the class width. For example, if you choose a class width of 0.5, the intervals would be 1.0-1.5, 1.5-2.0, etc.
Count Frequencies:
- Count how many earthquake magnitudes fall into each class interval.
Fill in the Table:
- Use the class intervals and their corresponding frequencies to fill in the table.
Assuming a class width of 0.5, the table might look like this:
\[
\begin{tabular}{c|c}
\hline Magnitude (Richter) & Frequency \\
\hline 1.0-1.5 & 5 \\
\hline 1.5-2.0 & 10 \\
\hline 2.0-2.5 & 15 \\
\hline 2.5-3.0 & 20 \\
\hline 3.0-3.5 & 15 \\
\hline 3.5-4.0 & 10 \\
\hline 4.0-4.5 & 5 \\
\hline
\end{tabular}
\]
To determine if the distribution is normal, consider the following:
- Symmetry: A normal distribution is symmetric around the mean. Check if the frequencies increase to a peak and then decrease symmetrically.
- Bell Shape: The distribution should resemble a bell curve.
- Empirical Rule: Approximately 68% of the data should fall within one standard deviation of the mean, 95% within two, and 99.7% within three.
The frequency distribution appears to be a normal distribution if the frequencies increase to a peak and then decrease symmetrically, forming a bell-shaped curve. If the distribution is skewed or has multiple peaks, it is not normal.
Without the actual data, this is a general guideline on how to construct the frequency distribution and assess its normality.