https://file.aiquickdraw.com/mathbot/file/17295570870261ybd5qiu.jpg

Let's analyze each description and match it with the appropriate histogram from the four options provided.

1. **The distribution of length measurements at birth for 10,000 babies**:
   This describes a normal distribution because most babies are likely to be close to the average length, with fewer babies at the extreme lengths. The histogram for this would be bell-shaped, which corresponds to **Histogram I**.

2. **The distribution of hours that students studied for an exam**:
   This distribution likely has two peaks: one for students who studied a lot and one for students who didn’t study much, with fewer students studying an average amount. This is a bimodal distribution, and **Histogram II** shows this pattern.

3. **The distribution of annual income for school employees where a high percentage of employees are entry-level teachers and only a few are high-paid administrators**:
   This is a right-skewed distribution, as most employees earn lower salaries, and only a small number earn high salaries. **Histogram IV** shows a right-skewed distribution.

4. **The distribution of quiz scores on an easy quiz**:
   In an easy quiz, most students would score high marks, and fewer students would score lower marks. This results in a left-skewed distribution. **Histogram III** shows this.

### Answers:
- For the distribution of length measurements at birth: **I**
- For the distribution of hours that students studied: **II**
- For the distribution of annual income for school employees: **IV**
- For the distribution of quiz scores on an easy quiz: **III**

Therefore, the correct matches are:
- a: I
- b: III
- c: II
- d: IV

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

Here are 5 related questions to further your understanding:
1. What defines a skewed distribution and how can you identify one visually?
2. How can you differentiate between bimodal and normal distributions?
3. What types of real-world data often follow a normal distribution?
4. Why might quiz scores on an easy test typically result in a left-skewed distribution?
5. How does sample size affect the appearance of a histogram?

**Tip**: When analyzing histograms, focus on the symmetry (or lack thereof) and the number of peaks to classify the distribution type.

Choose the histogram that matches the distribution of length measurements at birth for 10,000 babies, hours students studied for an exam, annual income distribution of school employees, and quiz scores on an easy quiz.

This math problem involves matching histograms to distributions, such as normal and skewed distributions. The data includes length measurements of babies, hours students studied for an exam, income distribution of school employees, and quiz scores on an easy quiz. Suitable for Grades 9-12.

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