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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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
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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