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The problem asks to find the proportion of daily Methadone dosages that are less than 100 milligrams based on the histogram provided. Let's break this down step by step:

### Step 1: Analyze the Histogram
The histogram shows the following information:
- The dosage intervals are 0–50 mg, 50–100 mg, 100–150 mg, 150–200 mg, and 200–250 mg.
- The frequencies for each interval are:
  - 0–50 mg: 4 patients
  - 50–100 mg: 7 patients
  - 100–150 mg: 8 patients
  - 150–200 mg: 4 patients
  - 200–250 mg: 2 patients

### Step 2: Focus on Dosages Less Than 100 mg
- The dosage intervals that are less than 100 mg are 0–50 mg and 50–100 mg.
- The number of patients with dosages in these intervals are:
  - 0–50 mg: 4 patients
  - 50–100 mg: 7 patients
- Total patients with dosage less than 100 mg = 4 + 7 = **11 patients**

### Step 3: Calculate the Proportion
The total number of patients in the study is 25. So, the proportion of patients with a dosage less than 100 mg is:

\[
\text{Proportion} = \frac{11}{25} = 0.44
\]

### Answer:
The proportion of daily dosages that are less than 100 mg is **0.44**.

Would you like any further details or have any questions?

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Here are 5 related questions to expand on this:
1. What is the proportion of patients with dosages between 100 mg and 200 mg?
2. How would you calculate the mean dosage based on the histogram?
3. Can you determine the median dosage range from the histogram?
4. What is the proportion of patients receiving dosages greater than 150 mg?
5. How would you represent this data as a cumulative frequency graph?

**Tip:** Histograms are great for visualizing frequency distributions, but always ensure that you have a good understanding of what the intervals represent when analyzing proportions.

Based on the histogram, find the proportion of daily dosages in the sample that are less than 100 milligrams. Write your answer as a decimal, and do not round your answer.

Learn how to find the proportion of Methadone dosages less than 100 milligrams based on histogram data. This example covers key statistical concepts such as histogram analysis and proportion calculation. Suitable for students in Grades 9-12.

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