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.)
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.)
MATLAB: An Introduction with Applications
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd210f98b-1208-4eea-a54e-043fbbd49724%2F02531d1a-275c-469b-bb11-943dae836445%2F7750ac7.png&w=3840&q=75)
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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