A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 8 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. O B. The trials are not independent. OC. The experiment consists of only identical trials. 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 = 5). P(x = 5) = (Round to four decimal places as needed.) e. Find the probability that 2 or fewer of the 8 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 8 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. O B. The trials are not independent. OC. The experiment consists of only identical trials. 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 = 5). P(x = 5) = (Round to four decimal places as needed.) e. Find the probability that 2 or fewer of the 8 adults do not work during summer vacation. P(xs2) = (Round to four decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A poll found that
15%
of adults do not work at all while on summer vacation. In a random sample of
8
adults, let x represent the number who do not work during summer vacation. Complete parts a through
e.
![## Binomial Probability Example
A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let \( x \) represent the number who do not work during summer vacation. Complete parts a through e.
### Part A: Define Success in the Experiment
For this experiment, define the event that represents a "success." Choose the correct answer below.
- \( \bigcirc \) Adults working during summer vacation
- \( \bigcirc \) Adults not working during summer vacation
### Part B: Determine Why \( x \) is a Binomial Random Variable
Explain why \( x \) is (approximately) a binomial random variable. Choose the correct answer below.
- \( \bigcirc \) A. There are three possible outcomes on each trial.
- \( \bigcirc \) B. The trials are not independent.
- \( \bigcirc \) C. The experiment consists of only identical trials.
- \( \bigcirc \) 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.
### Part C: Find the Probability \( p \)
Give the value of \( p \) for this binomial experiment.
\[ p = \_\_\_\_ \]
### Part D: Calculate \( P(x = 5) \)
Find \( P(x = 5) \).
\[ P(x = 5) = \_\_\_\_ \quad (\text{Round to four decimal places as needed.}) \]
### Part E: Calculate \( P(x \leq 2) \)
Find the probability that 2 or fewer of the 8 adults do not work during summer vacation.
\[ P(x \leq 2) = \_\_\_\_ \quad (\text{Round to four decimal places as needed.}) \]
*This exercise demonstrates how to apply the binomial probability formula in a real-world context.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2Fbbfaf805-070f-4dfd-a9d8-e4312b987c00%2F78wucb_processed.png&w=3840&q=75)
Transcribed Image Text:## Binomial Probability Example
A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let \( x \) represent the number who do not work during summer vacation. Complete parts a through e.
### Part A: Define Success in the Experiment
For this experiment, define the event that represents a "success." Choose the correct answer below.
- \( \bigcirc \) Adults working during summer vacation
- \( \bigcirc \) Adults not working during summer vacation
### Part B: Determine Why \( x \) is a Binomial Random Variable
Explain why \( x \) is (approximately) a binomial random variable. Choose the correct answer below.
- \( \bigcirc \) A. There are three possible outcomes on each trial.
- \( \bigcirc \) B. The trials are not independent.
- \( \bigcirc \) C. The experiment consists of only identical trials.
- \( \bigcirc \) 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.
### Part C: Find the Probability \( p \)
Give the value of \( p \) for this binomial experiment.
\[ p = \_\_\_\_ \]
### Part D: Calculate \( P(x = 5) \)
Find \( P(x = 5) \).
\[ P(x = 5) = \_\_\_\_ \quad (\text{Round to four decimal places as needed.}) \]
### Part E: Calculate \( P(x \leq 2) \)
Find the probability that 2 or fewer of the 8 adults do not work during summer vacation.
\[ P(x \leq 2) = \_\_\_\_ \quad (\text{Round to four decimal places as needed.}) \]
*This exercise demonstrates how to apply the binomial probability formula in a real-world context.*
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