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Let's analyze and solve the questions from the image step by step:

### Given Data
The problem provides a list of 40 student checking account balances:

`404, 74, 234, 149, 279, 215, 123, 55, 43, 321, 87, 234, 68, 489, 57, 185, 141, 758, 72, 863, 703, 125, 350, 440, 37, 252, 127, 608, 913, 302, 968, 712, 503, 489, 327, 608, 358, 425, 203, 127`

### Question Breakdown:

#### a. Organice los datos en una distribución de frecuencias utilizando 100 dólares como intervalo de clase y cero como punto de partida.

To solve this, we will create a frequency distribution with class intervals of 100 dollars, starting at 0.

#### b. Elabore un polígono de frecuencias acumulativas.

We will create a cumulative frequency polygon using the data from part (a).

#### c. Calcule el porcentaje de clientes preferentes.

A "preferred customer" is defined as one with a final balance of $400 or more. We will calculate the percentage of customers that fall into this category.

#### d. Calcule el cargo por servicio para los saldos finales más bajos.

The bank charges a 10% service fee on the lowest final balances. We will calculate which balances are charged and determine the amount.

### Let's solve each step:

#### a. Frequency Distribution with 100-dollar class intervals

We will organize the data into bins of 100 units starting from 0. Here is the step-by-step solution:

1. Data ranges from 0 to 1000.
2. Intervals: \[0-99\], \[100-199\], \[200-299\], ..., \[900-999\].

Let's calculate this in the next step.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the steps to solve each part of the problem manually. 

Here’s how you can approach it:

### a. Frequency Distribution with 100-Dollar Class Intervals
1. **Define Intervals**: Start with 0 and create intervals of 100 dollars: \[0-99\], \[100-199\], \[200-299\], and so on, up to \[900-999\].
2. **Count Frequencies**: Count how many balances fall into each interval.

### b. Cumulative Frequency Polygon
1. **Calculate Cumulative Frequencies**: Add the frequencies from the previous step cumulatively.
2. **Plot the Polygon**: Create a graph with intervals on the x-axis and cumulative frequencies on the y-axis.

### c. Percentage of "Preferred" Customers
1. **Count Customers with Balance ≥ 400**: Find how many balances are 400 or more.
2. **Calculate Percentage**: \[(Number of Preferred Customers / Total Customers) * 100\].

### d. Service Charge for Low Balances
1. **Determine Lowest Balances**: Identify which balances are subject to the 10% charge.
2. **Calculate Charge**: Multiply these balances by 10% to find the service charge.

If you want to try solving these steps on your own or need any further help or details, let me know!

### Related Questions
1. How can you create a histogram for the frequency distribution?
2. What is the mode of the balance data, and how do you find it?
3. How do you interpret the cumulative frequency polygon?
4. What are the benefits of using frequency distributions in data analysis?
5. How would the results change if a different interval size were chosen?

### Tip
When calculating frequencies, always ensure that each data point is counted in only one interval to avoid errors in your analysis.

Midland National Bank seleccionó una muestra de 40 cuentas de cheques de estudiantes. A continuación aparecen sus saldos de fin de mes. Organice los datos en una distribución de frecuencias utilizando 100 dólares como intervalo de clase y cero como punto de partida. Elabore un polígono de frecuencias acumulativas. Calcule el porcentaje de clientes preferentes. El banco hace un cargo por servicio de 10% a los saldos finales más bajos. ¿Qué cantidad recomendaría como punto límite entre los que pagan un cargo por servicio y los que no lo hacen?

Organize 40 student bank account balances into a frequency distribution with 100-dollar intervals and create a cumulative frequency polygon. Calculate the percentage of preferred customers with balances of $400 or more and determine the 10% service charge for the lowest balances.

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