A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 9 adults, let x represent the number who do not work during summer vacation. Complete parts a through e. a. For this experiment, define the event that represents a "success." Choose the correct answer below. O Adults working during summer vacation O Adults not working during summer vacation b. Explain why x is (approximately) a binomial random variable. Choose the correct answer below. O A. There are three possible outcomes on each trial. B. The experiment consists of only identical trials. C. The trials are not independent. O D. The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. c. Give the value of p for this binomial experiment. p = d. Find P(x= 3). %3D P(x= 3) = (Round to four decimal places as needed.) e. Find the probability that 2 or fewer of the 9 adults do not work during summer vacation. P(xs2)= (Round to four decimal places as needed.)

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**Examining a Poll on Adult Work Patterns During Summer Vacation**

A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 9 adults, let \( x \) represent the number who do not work during summer vacation. Complete parts a through e below.

### a. Defining Success in This Experiment
For this experiment, define the event that represents a "success." Choose the correct answer below:
- O Adults working during summer vacation
- O Adults not working during summer vacation

### b. Characteristics of a Binomial Random Variable
Explain why \( x \) is (approximately) a binomial random variable. Choose the correct answer below:
- O A. There are three possible outcomes on each trial.
- O B. The experiment consists of only identical trials.
- O C. The trials are not independent.
- O D. The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent.

### c. Determining the Value of \( p \)
Give the value of \( p \) for this binomial experiment.
\[ p = \ \_\_\_\_ \]

### d. Calculating Specific Probability
Find \( P(x = 3) \).
\[ P(x = 3) = \ \_\_\_\_ \ (Round \ to \ four \ decimal \ places \ as \ needed.) \]

### e. Finding Cumulative Probability
Find the probability that 2 or fewer of the 9 adults do not work during summer vacation.
\[ P(x \le 2) = \ \_\_\_\_ \ (Round \ to \ four \ decimal \ places \ as \ needed.) \]

### Explanations:

#### Available Choices and Correct Answers:
- **Part a:**
  Adults not working during summer vacation

- **Part b:**
  D. The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent.

#### Values to Determine:
- **Part c:** 
  \( p \) is the probability that a randomly selected adult does not work during summer vacation.

  Given: 
  \[ 15\% \text{or} 0.15 \]
  Hence, 
  \[ p = 0.15 \]

- **Part d:** 
  Use the
Transcribed Image Text:**Examining a Poll on Adult Work Patterns During Summer Vacation** A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 9 adults, let \( x \) represent the number who do not work during summer vacation. Complete parts a through e below. ### a. Defining Success in This Experiment For this experiment, define the event that represents a "success." Choose the correct answer below: - O Adults working during summer vacation - O Adults not working during summer vacation ### b. Characteristics of a Binomial Random Variable Explain why \( x \) is (approximately) a binomial random variable. Choose the correct answer below: - O A. There are three possible outcomes on each trial. - O B. The experiment consists of only identical trials. - O C. The trials are not independent. - O D. The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. ### c. Determining the Value of \( p \) Give the value of \( p \) for this binomial experiment. \[ p = \ \_\_\_\_ \] ### d. Calculating Specific Probability Find \( P(x = 3) \). \[ P(x = 3) = \ \_\_\_\_ \ (Round \ to \ four \ decimal \ places \ as \ needed.) \] ### e. Finding Cumulative Probability Find the probability that 2 or fewer of the 9 adults do not work during summer vacation. \[ P(x \le 2) = \ \_\_\_\_ \ (Round \ to \ four \ decimal \ places \ as \ needed.) \] ### Explanations: #### Available Choices and Correct Answers: - **Part a:** Adults not working during summer vacation - **Part b:** D. The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. #### Values to Determine: - **Part c:** \( p \) is the probability that a randomly selected adult does not work during summer vacation. Given: \[ 15\% \text{or} 0.15 \] Hence, \[ p = 0.15 \] - **Part d:** Use the
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