The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Foum randomly selected adult Americans are examined for psychiatric disorders. Let the number of adults who suffers from psychiatric disast be represented by the random variable, X

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### Probability Distribution of Adults with Psychiatric Disorders

The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult Americans are examined for psychiatric disorders. Let the number of adults who suffer from psychiatric disorders be represented by the random variable, \( X \).

1. **Number of trials (\( n \))**:
   \( n = 4 \)

2. **Probability of success (\( p \))**:
   \( p = 0.20 \)
   (Round to 4 decimal places)

3. **Probability of failure (\( 1 - p \))**:
   \( 1 - p = 0.64 \)
   (Round to 4 decimal places)

4. **Probability Distribution Table**:
    Prepare the probability distribution for the random variable \( X \). Complete the following table. Round your answers to 4 decimal places, e.g. 0.XXXX or .XXXX.

| \( X = x \) | \( P(X = x) \) |
|-------------|----------------|
| 0           | 0.4096         |
| 1           | 0.4096         |
| 2           | 0.1536         |
| 3           |                |
| 4           |                |

Please fill in the remaining probabilities to complete the table.
Transcribed Image Text:### Probability Distribution of Adults with Psychiatric Disorders The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult Americans are examined for psychiatric disorders. Let the number of adults who suffer from psychiatric disorders be represented by the random variable, \( X \). 1. **Number of trials (\( n \))**: \( n = 4 \) 2. **Probability of success (\( p \))**: \( p = 0.20 \) (Round to 4 decimal places) 3. **Probability of failure (\( 1 - p \))**: \( 1 - p = 0.64 \) (Round to 4 decimal places) 4. **Probability Distribution Table**: Prepare the probability distribution for the random variable \( X \). Complete the following table. Round your answers to 4 decimal places, e.g. 0.XXXX or .XXXX. | \( X = x \) | \( P(X = x) \) | |-------------|----------------| | 0 | 0.4096 | | 1 | 0.4096 | | 2 | 0.1536 | | 3 | | | 4 | | Please fill in the remaining probabilities to complete the table.
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