Homework Help is Here – Start Your Trial Now!
Math
Statistics
A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey found that 85% of parents of teenagers have taken their teenager's cell phone or Internet privileges away as a punishment. You randomly select 14 parents of teenagers and ask them whether they have taken their teenager's cell phone or Internet privileges away as a punishment. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. O A. Yes, the mean is and the standard deviation is (Round to two decimal places as needed.) O B. No, because nq < 5. O C. No, because np < 5.

A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey found that 85% of parents of teenagers have taken their teenager's cell phone or Internet privileges away as a punishment. You randomly select 14 parents of teenagers and ask them whether they have taken their teenager's cell phone or Internet privileges away as a punishment. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. O A. Yes, the mean is and the standard deviation is (Round to two decimal places as needed.) O B. No, because nq < 5. O C. No, because np < 5.

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
Problem 1P
See similar textbooks
icon
Related questions
Question
Please answer the following 2 questions
**Educational Text: Understanding Binomial Distributions and Normal Approximation** **Problem 5.5.18** In this problem, we explore whether we can use the normal distribution to approximate a binomial distribution. To do this, we need to consider the mean and standard deviation of the data provided. Here’s the scenario: A survey reveals that 85% of parents of teenagers have taken away their teenager's cell phone or Internet privileges as a punishment. You randomly select 14 parents of teenagers and ask them whether they have done this. **Deciding on Normal Approximation:** When deciding if you can approximate a binomial distribution with a normal distribution, you need to consider the conditions where `np` and `nq` (where q = 1-p) are both greater than 5. - **p** (the probability of success) = 0.85 - **n** (the number of trials) = 14 Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice: - **A.** Yes, the mean is [Box] and the standard deviation is [Box]. (Round to two decimal places as needed.) - **B.** No, because nq < 5. - **C.** No, because np < 5. **Solution Approach:** To proceed, calculate: 1. **Mean (μ):** \( \mu = np \) 2. **Standard Deviation (σ):** \( \sigma = \sqrt{npq} \) Use these formulas to solve and determine whether both np and nq are greater than 5 to validate normal approximation. If they are, calculate and fill in the mean and standard deviation for a valid approximation. If not, select the correct rationale depending on which condition is not satisfied.
Transcribed Image Text:**Educational Text: Understanding Binomial Distributions and Normal Approximation** **Problem 5.5.18** In this problem, we explore whether we can use the normal distribution to approximate a binomial distribution. To do this, we need to consider the mean and standard deviation of the data provided. Here’s the scenario: A survey reveals that 85% of parents of teenagers have taken away their teenager's cell phone or Internet privileges as a punishment. You randomly select 14 parents of teenagers and ask them whether they have done this. **Deciding on Normal Approximation:** When deciding if you can approximate a binomial distribution with a normal distribution, you need to consider the conditions where `np` and `nq` (where q = 1-p) are both greater than 5. - **p** (the probability of success) = 0.85 - **n** (the number of trials) = 14 Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice: - **A.** Yes, the mean is [Box] and the standard deviation is [Box]. (Round to two decimal places as needed.) - **B.** No, because nq < 5. - **C.** No, because np < 5. **Solution Approach:** To proceed, calculate: 1. **Mean (μ):** \( \mu = np \) 2. **Standard Deviation (σ):** \( \sigma = \sqrt{npq} \) Use these formulas to solve and determine whether both np and nq are greater than 5 to validate normal approximation. If they are, calculate and fill in the mean and standard deviation for a valid approximation. If not, select the correct rationale depending on which condition is not satisfied.
The text describes a survey conducted among adults aged 33 to 51 in Country A regarding sports participation. According to the survey, 70% of adults reported participating in at least one sport. When selecting a random sample of 350 people in this age group, it was found that 40% reported participating in at least one sport. The question posed is about the likelihood and representativeness of this sample. Following the text, there are multiple-choice options asking readers to determine the likelihood of the survey results based on probability, specifically if it is greater or less than 0.05. The options are: A. The result is highly unlikely because its probability is greater than 0.05. Thus, the sample is a good representative sample. B. The result is highly likely because its probability is greater than 0.05. Thus, the sample is not a good representative sample. C. The result is highly unlikely because its probability is less than 0.05. Thus, the sample is not a good representative sample. D. The result is highly likely because its probability is less than 0.05. Thus, the sample is not a good representative sample. Additionally, there is an image of a bar chart titled "How adults get physical,” showing the preference percentages for different sports: - Swimming: 16% - Bicycling, golf: 12% - Hiking: 11% - Softball, walking: 10% - Fishing: 9% - Tennis: 6% - Bowling, running: 4% - Aerobics: 2% This data is useful for understanding the distribution of sports participation among the surveyed adults.
Transcribed Image Text:The text describes a survey conducted among adults aged 33 to 51 in Country A regarding sports participation. According to the survey, 70% of adults reported participating in at least one sport. When selecting a random sample of 350 people in this age group, it was found that 40% reported participating in at least one sport. The question posed is about the likelihood and representativeness of this sample. Following the text, there are multiple-choice options asking readers to determine the likelihood of the survey results based on probability, specifically if it is greater or less than 0.05. The options are: A. The result is highly unlikely because its probability is greater than 0.05. Thus, the sample is a good representative sample. B. The result is highly likely because its probability is greater than 0.05. Thus, the sample is not a good representative sample. C. The result is highly unlikely because its probability is less than 0.05. Thus, the sample is not a good representative sample. D. The result is highly likely because its probability is less than 0.05. Thus, the sample is not a good representative sample. Additionally, there is an image of a bar chart titled "How adults get physical,” showing the preference percentages for different sports: - Swimming: 16% - Bicycling, golf: 12% - Hiking: 11% - Softball, walking: 10% - Fishing: 9% - Tennis: 6% - Bowling, running: 4% - Aerobics: 2% This data is useful for understanding the distribution of sports participation among the surveyed adults.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Research Ethics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS