In the probability distribution to the right, the random variable X represents the number of hits a baseball player obtained in a game over the course of a season. Complete parts (a) through (f) below. P(x) O 0.1663 1 0.3351 2 0.2862 3 0.1495 0.0375 0.0254 5 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because V between and , inclusive, and the V of the probabilities is. (Type whole numbers. Use ascending order.)

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In the probability distribution table provided, the random variable \( X \) represents the number of hits a baseball player achieved in a game during a season. The data is to be analyzed by completing tasks (a) through (f).

### Probability Distribution Table

| \( x \) | \( P(x) \) |
|---------|------------|
| 0       | 0.1663     |
| 1       | 0.3351     |
| 2       | 0.2862     |
| 3       | 0.1495     |
| 4       | 0.0375     |
| 5       | 0.0254     |

### Task (a): Verify that this is a discrete probability distribution.
- Instructions: Confirm that the given distribution is discrete by completing the statements:
  - This is a discrete probability distribution because the number of hits is an integer between \(\_\_\_\_\) and \(\_\_\_\_\), inclusive, and the sum of the probabilities is \(\_\_\_\_\).

### Task (b): Draw a graph of the probability distribution and describe its shape.
- Instructions:
  - Select the correct graph of the probability distribution from the options (A, B, C, D) below.
  - Describe the shape of the distribution.
  - **Graphs Description**:
    - Graph A: Bars represent probabilities for hits 0 through 5, highest at 1 hit.
    - Graph B: Similar to Graph A, slightly varied probabilities.
    - Graph C: Probabilities increase towards 3 and then decrease.
    - Graph D: Symmetrical distribution around 2.

- Describe the distribution as either symmetric, skewed left, or skewed right, and determine if it is uniform, bell-shaped, etc.

(Note: The textual portion should be filled out based on instructions in a classroom or exam setting, with students completing the boxed spaces.)

### Additional tasks (not visible here) likely include:
- Calculating the mean of the distribution.
- Determining the variance and standard deviation.
- Solving related probabilities based on the distribution.

This activity involves verifying, graphing, and analyzing a discrete probability distribution related to sports statistics.
Transcribed Image Text:In the probability distribution table provided, the random variable \( X \) represents the number of hits a baseball player achieved in a game during a season. The data is to be analyzed by completing tasks (a) through (f). ### Probability Distribution Table | \( x \) | \( P(x) \) | |---------|------------| | 0 | 0.1663 | | 1 | 0.3351 | | 2 | 0.2862 | | 3 | 0.1495 | | 4 | 0.0375 | | 5 | 0.0254 | ### Task (a): Verify that this is a discrete probability distribution. - Instructions: Confirm that the given distribution is discrete by completing the statements: - This is a discrete probability distribution because the number of hits is an integer between \(\_\_\_\_\) and \(\_\_\_\_\), inclusive, and the sum of the probabilities is \(\_\_\_\_\). ### Task (b): Draw a graph of the probability distribution and describe its shape. - Instructions: - Select the correct graph of the probability distribution from the options (A, B, C, D) below. - Describe the shape of the distribution. - **Graphs Description**: - Graph A: Bars represent probabilities for hits 0 through 5, highest at 1 hit. - Graph B: Similar to Graph A, slightly varied probabilities. - Graph C: Probabilities increase towards 3 and then decrease. - Graph D: Symmetrical distribution around 2. - Describe the distribution as either symmetric, skewed left, or skewed right, and determine if it is uniform, bell-shaped, etc. (Note: The textual portion should be filled out based on instructions in a classroom or exam setting, with students completing the boxed spaces.) ### Additional tasks (not visible here) likely include: - Calculating the mean of the distribution. - Determining the variance and standard deviation. - Solving related probabilities based on the distribution. This activity involves verifying, graphing, and analyzing a discrete probability distribution related to sports statistics.
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