Question

What is the marginal distribution of females
Underweight 37 at goal 446 overweight 137

Answer 1

To find the marginal distribution of females with respect to weight categories (Underweight, At goal, and Overweight), we first need to categorize the provided information:

- Underweight: 37
- At goal: 446
- Overweight: 137

The total number of females can be calculated as follows:

\[
\text{Total females} = \text{Underweight} + \text{At goal} + \text{Overweight} = 37 + 446 + 137 = 620
\]

Now, we can calculate the marginal distribution for each category by dividing the number in each category by the total number of females:

1. **Underweight**:
\[
P(\text{Underweight}) = \frac{37}{620} \approx 0.0597 \text{ or } 5.97\%
\]

2. **At goal**:
\[
P(\text{At goal}) = \frac{446}{620} \approx 0.7194 \text{ or } 71.94\%
\]

3. **Overweight**:
\[
P(\text{Overweight}) = \frac{137}{620} \approx 0.2209 \text{ or } 22.09\%
\]

So, the marginal distribution of females across the weight categories is approximately:
- Underweight: 5.97%
- At goal: 71.94%
- Overweight: 22.09%