The histogram shows distances between a group a. How many observations are there? b. What is the greatest interval in distance stude lived from the school? How many students lived more than 6 miles fr the school? \( 8+4 \) ? \( =7 \) What percent of the students live at most 6 mi

To assist you effectively with the questions related to the histogram showing distances students live from the school, I'll outline how to approach each part. However, to provide exact numerical answers, I would need the specific data from the histogram (i.e., the intervals and the corresponding number of students in each interval). Here's a general guide on how to tackle each question: --- ### a. **How Many Observations Are There?** **Approach:** - **Identify All Intervals:** Look at each distance interval presented in the histogram. - **Sum the Frequencies:** Add up the number of students (frequency) in each interval to get the total number of observations. **Example:** If the histogram has intervals like: - 0-2 miles: 5 students - 2-4 miles: 8 students - 4-6 miles: 7 students - 6-8 miles: 4 students Total Observations = 5 + 8 + 7 + 4 = **24 students** --- ### b. **What Is the Greatest Interval in Distance Students Lived from the School?** **Approach:** - **Determine Interval Widths:** Calculate the width of each interval by subtracting the lower bound from the upper bound. - **Identify the Largest Width:** The interval with the largest width represents the greatest span of distances covered. **Example:** Using the intervals above: - Each interval (0-2, 2-4, etc.) has a width of 2 miles. - If another set of intervals like 0-3, 3-6, 6-9 were used, the width would be 3 miles. The **greatest interval** is the one with the largest width (e.g., 0-3 miles if using 0-3, 3-6, 6-9). --- ### c. **How Many Students Lived More Than 6 Miles from the School?** **Approach:** - **Identify Relevant Intervals:** Look for intervals where the lower bound is greater than 6 miles. - **Sum Their Frequencies:** Add the number of students in these intervals. **Example:** Using the initial intervals: - 6-8 miles: 4 students Thus, **4 students** live more than 6 miles from the school. --- ### d. **Clarification on the Expression \( 8 + 4 = 7 \)** It appears there might be a typographical error in this part of the question. Typically, \( 8 + 4 \) equals **12**, not 7. If this was intended to reference frequencies or another aspect of the histogram, please provide additional context or clarify the question so I can assist you accurately. --- ### e. **What Percent of the Students Live at Most 6 Miles from the School?** **Approach:** - **Identify Relevant Intervals:** Find all intervals where the upper bound is **6 miles or less**. - **Sum Their Frequencies:** Add the number of students in these intervals. - **Calculate the Percentage:** Divide this sum by the total number of observations and multiply by 100. **Formula:** \[ \text{Percentage} = \left( \frac{\text{Number of students living ≤6 miles}}{\text{Total number of students}} \right) \times 100\% \] **Example:** Using the initial intervals: - 0-2 miles: 5 students - 2-4 miles: 8 students - 4-6 miles: 7 students Total living at most 6 miles = 5 + 8 + 7 = **20 students** If Total Observations = 24 students, \[ \text{Percentage} = \left( \frac{20}{24} \right) \times 100\% \approx 83.33\% \] So, approximately **83.33%** of the students live at most 6 miles from the school. --- **If you can provide the specific data from the histogram**, I can give you precise numerical answers to each of these questions. Otherwise, I hope this general guide helps you understand how to approach each part of your problem!