A recent poll of over 2,000 adults was designed to answer the question "Are adults superstitious?" One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-forth of adults (25%) believe finding and picking up a penny is good luck. Consider a random sample of 15 adults and let x represent the number who believe finding and picking up a penny is good luck. Complete parts a though f below. from person to person and each survey response is independent of each other. O C. Binomial random variables are always obtained through sampling. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey does not change from person to person and each survey response is dependent of all the previous responses. O D. Sampling 2000 adults is equivalent to performing a dice-roll type experiment. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The surveý changes from person to person and each survey response is independent of each other. c. Give the value of p for this binomial experiment. p= 0.25 (Round to two decimal places as needed.) d. Find P(x<5). P(x<5) = 0.687 (Round to three decimal places as needed.) e. Find P(x = 6). P(x = 6) = 0.092 (Round to three decimal places as needed.) f. Find P(x>2). Riy 21- O (Round to three decimal places ae needed
A recent poll of over 2,000 adults was designed to answer the question "Are adults superstitious?" One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-forth of adults (25%) believe finding and picking up a penny is good luck. Consider a random sample of 15 adults and let x represent the number who believe finding and picking up a penny is good luck. Complete parts a though f below. from person to person and each survey response is independent of each other. O C. Binomial random variables are always obtained through sampling. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey does not change from person to person and each survey response is dependent of all the previous responses. O D. Sampling 2000 adults is equivalent to performing a dice-roll type experiment. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The surveý changes from person to person and each survey response is independent of each other. c. Give the value of p for this binomial experiment. p= 0.25 (Round to two decimal places as needed.) d. Find P(x<5). P(x<5) = 0.687 (Round to three decimal places as needed.) e. Find P(x = 6). P(x = 6) = 0.092 (Round to three decimal places as needed.) f. Find P(x>2). Riy 21- O (Round to three decimal places ae needed
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![**Binomial Probability and Superstitions: An Educational Exploration**
---
**Overview:**
A recent poll surveyed over 2,000 adults to investigate the question: "Are adults superstitious?" One item in the survey addressed the belief "see a penny, pick it up, all day long you'll have good luck." The poll determined that 25% (one-fourth) of adults hold this belief. We will consider a random sample of 15 adults and let \( x \) represent the number who believe that finding and picking up a penny is good luck. We aim to study the binomial distribution applied to this scenario.
**Binomial Experiment Assumptions:**
A binomial experiment satisfies the following criteria:
- There is a fixed number of trials.
- Each trial has two possible outcomes: success or failure.
- The probability of success is the same for each trial.
- Trials are independent of each other.
**Evaluate Statements Regarding the Poll:**
1. **Statement C:**
- Binomial random variables are always obtained through sampling. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey does not change from person to person and each survey response is dependent on all the previous responses.
2. **Statement D (False):**
- Sampling 2000 adults is equivalent to performing a dice-roll type experiment. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey changes from person to person and each survey response is independent of each other.
**Calculations:**
a. **Determine the probability of success (p) for this binomial experiment:**
\( p = 0.25 \)
(Rounded to two decimal places as needed.)
b. **Find \( P(x < 5) \):**
\( P(x < 5) = 0.687 \)
(Rounded to three decimal places as needed.)
c. **Find \( P(x = 6) \):**
\( P(x = 6) = 0.092 \)
(Rounded to three decimal places as needed.)
d. **Find \( P(x \geq 2) \):**
\( P(x \geq 2) = \)
(Rounded to three decimal places as needed.)
---
This educational content explores the binomial probability distribution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb25aa5e3-8edb-4708-bfd5-abf65dd8da34%2F42a36f03-c444-46df-b5f2-9b66bc12a4d2%2Ft213q4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Binomial Probability and Superstitions: An Educational Exploration**
---
**Overview:**
A recent poll surveyed over 2,000 adults to investigate the question: "Are adults superstitious?" One item in the survey addressed the belief "see a penny, pick it up, all day long you'll have good luck." The poll determined that 25% (one-fourth) of adults hold this belief. We will consider a random sample of 15 adults and let \( x \) represent the number who believe that finding and picking up a penny is good luck. We aim to study the binomial distribution applied to this scenario.
**Binomial Experiment Assumptions:**
A binomial experiment satisfies the following criteria:
- There is a fixed number of trials.
- Each trial has two possible outcomes: success or failure.
- The probability of success is the same for each trial.
- Trials are independent of each other.
**Evaluate Statements Regarding the Poll:**
1. **Statement C:**
- Binomial random variables are always obtained through sampling. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey does not change from person to person and each survey response is dependent on all the previous responses.
2. **Statement D (False):**
- Sampling 2000 adults is equivalent to performing a dice-roll type experiment. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey changes from person to person and each survey response is independent of each other.
**Calculations:**
a. **Determine the probability of success (p) for this binomial experiment:**
\( p = 0.25 \)
(Rounded to two decimal places as needed.)
b. **Find \( P(x < 5) \):**
\( P(x < 5) = 0.687 \)
(Rounded to three decimal places as needed.)
c. **Find \( P(x = 6) \):**
\( P(x = 6) = 0.092 \)
(Rounded to three decimal places as needed.)
d. **Find \( P(x \geq 2) \):**
\( P(x \geq 2) = \)
(Rounded to three decimal places as needed.)
---
This educational content explores the binomial probability distribution
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