The data given below show the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b). Overtime hours 1 2 3 4. 6. Employees 10 29 54 46 26 15 (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (a) Construct the probability distribution by completing the table below. 1 3 4 5 P(x) (Round to three decimal places as needed.)

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# Analyzing Overtime Hours

The data below shows the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b).

### Overtime Hours Data

- **Overtime Hours:** 0, 1, 2, 3, 4, 5, 6
- **Employees:** 8, 10, 29, 54, 46, 26, 15

### Tasks

#### (a) Construct a Probability Distribution

To create the probability distribution, complete the table below using the provided data. Round to three decimal places as needed.

| x  | P(x) |
|---|------|
| 0 |      |
| 1 |      |
| 2 |      |
| 3 |      |
| 4 |      |
| 5 |      |
| 6 |      |

#### (b) Graph the Probability Distribution

Four graphs (A, B, C, D) are given to represent the probability distribution of the overtime hours. Each graph features:

- **X-axis:** Overtime Hours (0 to 6)
- **Y-axis:** Probability (0 to 0.4)

The task is to:

- **Choose the correct graph:** Select which histogram correctly represents the probability distribution based on the calculated probabilities.
- **Describe the distribution's shape:** Options are provided to describe whether the distribution is approximately symmetric, skewed left, or skewed right.

### Graph Options:

- **Graph A:** Symmetric bell-shaped distribution.
- **Graph B:** Skewed left distribution.
- **Graph C:** Skewed right distribution.
- **Graph D:** Increasing distribution.

### Shape Description
Choose the correct answer for the distribution's shape:

- Approximately symmetric (but not uniform)
- Skewed left
- Skewed right

Select the appropriate descriptions and graphs based on your calculations to accurately analyze this data.
Transcribed Image Text:# Analyzing Overtime Hours The data below shows the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b). ### Overtime Hours Data - **Overtime Hours:** 0, 1, 2, 3, 4, 5, 6 - **Employees:** 8, 10, 29, 54, 46, 26, 15 ### Tasks #### (a) Construct a Probability Distribution To create the probability distribution, complete the table below using the provided data. Round to three decimal places as needed. | x | P(x) | |---|------| | 0 | | | 1 | | | 2 | | | 3 | | | 4 | | | 5 | | | 6 | | #### (b) Graph the Probability Distribution Four graphs (A, B, C, D) are given to represent the probability distribution of the overtime hours. Each graph features: - **X-axis:** Overtime Hours (0 to 6) - **Y-axis:** Probability (0 to 0.4) The task is to: - **Choose the correct graph:** Select which histogram correctly represents the probability distribution based on the calculated probabilities. - **Describe the distribution's shape:** Options are provided to describe whether the distribution is approximately symmetric, skewed left, or skewed right. ### Graph Options: - **Graph A:** Symmetric bell-shaped distribution. - **Graph B:** Skewed left distribution. - **Graph C:** Skewed right distribution. - **Graph D:** Increasing distribution. ### Shape Description Choose the correct answer for the distribution's shape: - Approximately symmetric (but not uniform) - Skewed left - Skewed right Select the appropriate descriptions and graphs based on your calculations to accurately analyze this data.
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