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To construct the frequency distribution for the given weights, let’s follow these steps:

1. **Determine Class Intervals**: 
   - Start with a lower limit of \(40 \, \text{kg}\).
   - Use a class width of \(10 \, \text{kg}\), so intervals will be: \(40-49.9\), \(50-59.9\), \(60-69.9\), etc.

2. **Count Frequencies** for each class by categorizing each data point in the provided list. 

3. **Analyze Normality**: After constructing the frequency table, we can look at the distribution shape to assess if it resembles a normal distribution.

Let’s proceed by categorizing the weights.

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### Frequency Distribution Table
Here's how the frequencies should be grouped based on the intervals and weights:

| Weight (kg) | Frequency |
|-------------|-----------|
| 40 - 49.9   |           |
| 50 - 59.9   |           |
| 60 - 69.9   |           |
| 70 - 79.9   |           |
| 80 - 89.9   |           |
| 90 - 99.9   |           |

I'll fill in the frequencies based on the weights.### Completed Frequency Distribution Table

| Weight (kg) | Frequency |
|-------------|-----------|
| 40 - 49.9   | 2         |
| 50 - 59.9   | 22        |
| 60 - 69.9   | 22        |
| 70 - 79.9   | 13        |
| 80 - 89.9   | 3         |
| 90 - 99.9   | 4         |

### Analysis of Distribution Shape
The frequencies are highest in the middle intervals (50-59.9 and 60-69.9), with lower frequencies at the tails, resembling a bell-shaped distribution. Thus, this data may approximate a normal distribution, although further statistical tests (such as the Shapiro-Wilk test) would confirm this.

Would you like further details on the analysis or an explanation of normal distribution properties?

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#### Related Questions
1. How do you determine if a distribution is normal from a histogram?
2. What are the key properties of a normal distribution?
3. How would you calculate the mean and standard deviation for these weights?
4. What is the importance of class intervals in frequency distribution?
5. How can we visually assess normality using a frequency polygon?

#### Tip
When constructing frequency distributions, always ensure non-overlapping intervals for accurate data representation.

Weights of 67 college students in kilograms in September of freshman year are provided in the accompanying data set. Construct a frequency distribution. Begin with a lower class limit of 40 kg and use a class width of 10 kg. Does the distribution appear to be a normal distribution?

Learn how to construct a frequency distribution with a class width of 10 kg for a dataset of 67 student weights. This solution explains the steps to categorize data, determine frequencies, and assess the normality of the distribution. Ideal for students studying introductory statistics.

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