https://file.aiquickdraw.com/mathbot/file/1728989991186skohnku7.jpg

To solve this problem, we need to estimate the number of children who took 21 seconds or more to connect to the internet by analyzing the histogram and its frequency density information.

### Step 1: Breakdown of histogram data
From the histogram, the time intervals (in seconds) and their corresponding bar heights (representing frequency density) are as follows:
- **0 to 5 seconds**: Frequency density ≈ 1.2
- **5 to 10 seconds**: Frequency density ≈ 2.0
- **10 to 15 seconds**: Frequency density ≈ 3.6
- **15 to 20 seconds**: Frequency density ≈ 2.4
- **20 to 25 seconds**: Frequency density ≈ 1.2
- **25 to 30 seconds**: Frequency density ≈ 0.8
- **30 to 35 seconds**: Frequency density ≈ 0.4
- **35 to 40 seconds**: Frequency density ≈ 0.2

### Step 2: Total number of children and frequency calculation
The total number of children who took up to 12.5 seconds to connect is given as 110. We can use this information to calculate the frequencies for each bar. To find the frequency of a class, we multiply the class width by the frequency density.

#### Calculating frequencies for each class:
1. **0 to 5 seconds**:  
   \[
   \text{Frequency} = 5 \times 1.2 = 6
   \]
2. **5 to 10 seconds**:  
   \[
   \text{Frequency} = 5 \times 2.0 = 10
   \]
3. **10 to 15 seconds**:  
   \[
   \text{Frequency} = 5 \times 3.6 = 18
   \]
4. **15 to 20 seconds**:  
   \[
   \text{Frequency} = 5 \times 2.4 = 12
   \]
5. **20 to 25 seconds**:  
   \[
   \text{Frequency} = 5 \times 1.2 = 6
   \]
6. **25 to 30 seconds**:  
   \[
   \text{Frequency} = 5 \times 0.8 = 4
   \]
7. **30 to 35 seconds**:  
   \[
   \text{Frequency} = 5 \times 0.4 = 2
   \]
8. **35 to 40 seconds**:  
   \[
   \text{Frequency} = 5 \times 0.2 = 1
   \]

### Step 3: Estimate the number of children who took 21 seconds or more
We are interested in the children who took 21 seconds or more to connect. This falls within the intervals of **25 to 30**, **30 to 35**, and **35 to 40 seconds**.

By adding the frequencies of these intervals:
\[
\text{Total frequency} = 4 + 2 + 1 = 7
\]

Thus, the estimate for the number of children who took 21 seconds or more to connect to the internet is **7 children**.

---

Let me know if you'd like any further details or clarifications!

### Follow-up Questions:
1. How would you calculate the total number of children in the entire dataset?
2. What is the average time it took for children to connect to the internet based on this histogram?
3. How would the estimate change if the intervals were smaller, such as 2 seconds instead of 5 seconds?
4. How do frequency density and frequency differ in terms of their usage in histograms?
5. Can you identify the modal class from this histogram? Why?

### Tip:
Always check the class widths when interpreting histograms, as unequal widths can affect frequency calculations.

The histogram shows information about the time it took some children to connect to the internet. None of the children took more than 40 seconds to connect to the internet. 110 children took up to 12.5 seconds to connect to the internet. Work out an estimate for the number of children who took 21 seconds or more to connect to the internet.

Learn how to estimate the number of children who took 21 seconds or more to connect to the internet using a histogram. This problem involves key statistical concepts such as frequency density and estimation, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation