roups of adults are randomly selected and arranged in groups of three. he random variable x is the number in the group who say that they "ould feel comfortable in a self-driving vehicle. Determine whether a robability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, dentify the requirements that are not satisfied. X 0 1 2 3 OA. OF adult(s) (Round to one decimal place as needed.) OB. The table does not show a probability distribution. P(x) 0.367 0.425 0.186 0.022 CELL Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable x's number values are not associated with probabilities. C. No, the sum of all the probabilities is not equal to 1. D. No, not every probability is between 0 and 1 inclusive. E. No, the random variable x is categorical instead of numerical. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. H= adult(s) (Round to one decimal place as needed.) OB. The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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**Transcription for Educational Website**

**Description:**

Groups of adults are randomly selected and arranged in groups of three. The random variable \( x \) is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

| \( x \) | P(x)  |
|---------|-------|
| 0       | 0.367 |
| 1       | 0.425 |
| 2       | 0.186 |
| 3       | 0.022 |

**Questions:**

Does the table show a probability distribution? Select all that apply:

- [ ] A. Yes, the table shows a probability distribution.
- [ ] B. No, the random variable \( x \)'s number values are not associated with probabilities.
- [ ] C. No, the sum of all the probabilities is not equal to 1.
- [ ] D. No, not every probability is between 0 and 1 inclusive.
- [ ] E. No, the random variable \( x \) is categorical instead of numerical.

**Further Instructions:**

Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- [ ] A. \( \mu = \) [ ] adult(s) (Round to one decimal place as needed.)
- [ ] B. The table does not show a probability distribution.

Find the standard deviation of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- [ ] A. \( \sigma = \) [ ] adult(s) (Round to one decimal place as needed.)
- [ ] B. The table does not show a probability distribution.
Transcribed Image Text:**Transcription for Educational Website** **Description:** Groups of adults are randomly selected and arranged in groups of three. The random variable \( x \) is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. | \( x \) | P(x) | |---------|-------| | 0 | 0.367 | | 1 | 0.425 | | 2 | 0.186 | | 3 | 0.022 | **Questions:** Does the table show a probability distribution? Select all that apply: - [ ] A. Yes, the table shows a probability distribution. - [ ] B. No, the random variable \( x \)'s number values are not associated with probabilities. - [ ] C. No, the sum of all the probabilities is not equal to 1. - [ ] D. No, not every probability is between 0 and 1 inclusive. - [ ] E. No, the random variable \( x \) is categorical instead of numerical. **Further Instructions:** Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - [ ] A. \( \mu = \) [ ] adult(s) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. Find the standard deviation of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - [ ] A. \( \sigma = \) [ ] adult(s) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution.
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