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Let's break down the problem step by step based on the provided data in the image.

### Problem Summary:
A survey was conducted among 600 people aged 15 to 50. Of those:
- 150 people are aged between 15 and 24.
- 74% of those aged 15-24 prefer to stay up late rather than go to bed early.
- 55% of the total 600 people prefer to go to bed early.

The table is partially filled, and the goal is to:
1. Complete the cross table of frequencies.
2. Find the number of people aged between 25 and 50.
3. Determine how many people aged 15-24 prefer to stay up late.

### Step 1: Completing the Cross Table
Let's organize the data given:
- Total survey size: 600 people.
- Number of people aged 15-24: 150 people.
- 74% of these 150 people prefer staying up late: \( 150 \times 0.74 = 111 \) people.
- The remaining \( 150 - 111 = 39 \) people aged 15-24 prefer going to bed early.
- 55% of the total 600 people prefer going to bed early: \( 600 \times 0.55 = 330 \) people.
  - So, the number of people who prefer to stay up late is \( 600 - 330 = 270 \).

### Step 2: Determine the number of people aged between 25-50
Now, using the table and frequencies:
- From the total people who prefer going to bed early, 39 people are aged 15-24.
- Therefore, the remaining \( 330 - 39 = 291 \) people who prefer going to bed early must be aged 25-50.

### Step 3: Determine how many people aged 25-50 prefer to stay up late
- The total number of people who prefer to stay up late is 270.
- From these 270, 111 people are aged 15-24, so the remaining \( 270 - 111 = 159 \) people are aged 25-50.

### Final Table:
|                        | Se coucher tôt | Se coucher tard | Total |
|------------------------|----------------|-----------------|-------|
| **Entre 15 et 24 ans**  | 39             | 111             | 150   |
| **Entre 25 et 50 ans**  | 291            | 159             | 450   |
| **Total**               | 330            | 270             | 600   |

### Answers to Questions:
1. The table above is completed.
2. The number of people aged between 25 and 50 is 450.
3. The number of people aged 15-24 who prefer to stay up late is 111.

Would you like further details or explanations on any part of this? 

### Related Questions:
1. How do we calculate percentages based on survey data?
2. What other types of conditional probability could be used in similar problems?
3. How can we adjust the table if a new age group is added?
4. What would happen if the percentages of those who prefer to stay up late changed?
5. How would we compute the results if there was incomplete information?

### Tip:
Always start by identifying the total and subtotals in survey or frequency-based problems. It helps to create a structured approach to solving the problem!

We conducted a survey of 600 people aged 15 to 50. Among the 150 people aged 15 to 24, 74% prefer to stay up late rather than go to bed early. 55% of the respondents prefer to go to bed early. Complete the table of frequencies. 1. What is the number of people aged between 25 and 50? 2. How many people aged 15 to 24 prefer to stay up late?

Learn how to solve a conditional frequency table problem. This problem involves a survey of 600 people aged 15-50, where 55% prefer going to bed early. Understand how to complete the table and calculate the number of people aged 25-50 and 15-24 who prefer staying up late.

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