MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
9.
![**Educational Text: Understanding Binomial Distribution**
**Introduction:**
This exercise explores the concept of binomial distribution—a fundamental aspect of probability theory. We begin by considering the probabilities regarding the gender of newborns. Assume that each newborn baby has a probability of approximately 0.52 (52%) of being female and 0.48 (48%) of being male.
**Problem Statement:**
For a family with four children, let \( X \) represent the number of children who are girls. The following tasks are presented:
a. Identify the three conditions that must be satisfied for \( X \) to follow a binomial distribution.
b. Identify \( n \) and \( p \) for the binomial distribution.
c. Find the probability that the family has two girls and two boys.
**a. Conditions for a Binomial Distribution:**
The multiple-choice question asks which of the following conditions are necessary for a binomial distribution:
I. The \( n \) trials are independent.
II. Each trial has at least two possible outcomes.
III. The \( n \) trials are dependent.
IV. Each trial has the same probability of a success.
V. There are two trials.
VI. Each trial has two possible outcomes.
The correct answer is C: I, IV, and VI.
- I: The \( n \) trials should be independent.
- IV: Each trial should have the same probability of success.
- VI: Each trial should have precisely two possible outcomes (success/failure).
**b. Parameters for the Binomial Distribution:**
- \( n = 4 \): The number of trials (children).
- \( p = \): The probability of success (having a girl), which is 0.52.
**c. Probability of Two Girls and Two Boys:**
This section involves calculating the probability of obtaining exactly two girls and two boys. The solution would use the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
where \( \binom{n}{k} \) is the binomial coefficient.
**Conclusion:**
Understanding these conditions and calculations allows us to model real-world scenarios using binomial distribution effectively. By applying the conditions and formulas, predictions regarding probabilistic events can be made with more accuracy.](https://content.bartleby.com/qna-images/question/af10b40a-fae6-4e8b-9b89-0711a68556bc/e145f384-d5fd-4752-b2bc-841d84216a8d/v0d2058_processed.jpeg)
Transcribed Image Text:**Educational Text: Understanding Binomial Distribution**
**Introduction:**
This exercise explores the concept of binomial distribution—a fundamental aspect of probability theory. We begin by considering the probabilities regarding the gender of newborns. Assume that each newborn baby has a probability of approximately 0.52 (52%) of being female and 0.48 (48%) of being male.
**Problem Statement:**
For a family with four children, let \( X \) represent the number of children who are girls. The following tasks are presented:
a. Identify the three conditions that must be satisfied for \( X \) to follow a binomial distribution.
b. Identify \( n \) and \( p \) for the binomial distribution.
c. Find the probability that the family has two girls and two boys.
**a. Conditions for a Binomial Distribution:**
The multiple-choice question asks which of the following conditions are necessary for a binomial distribution:
I. The \( n \) trials are independent.
II. Each trial has at least two possible outcomes.
III. The \( n \) trials are dependent.
IV. Each trial has the same probability of a success.
V. There are two trials.
VI. Each trial has two possible outcomes.
The correct answer is C: I, IV, and VI.
- I: The \( n \) trials should be independent.
- IV: Each trial should have the same probability of success.
- VI: Each trial should have precisely two possible outcomes (success/failure).
**b. Parameters for the Binomial Distribution:**
- \( n = 4 \): The number of trials (children).
- \( p = \): The probability of success (having a girl), which is 0.52.
**c. Probability of Two Girls and Two Boys:**
This section involves calculating the probability of obtaining exactly two girls and two boys. The solution would use the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
where \( \binom{n}{k} \) is the binomial coefficient.
**Conclusion:**
Understanding these conditions and calculations allows us to model real-world scenarios using binomial distribution effectively. By applying the conditions and formulas, predictions regarding probabilistic events can be made with more accuracy.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps
Knowledge Booster
Similar questions
- General Solutions and Phase Portraits. In each of Problems 1 through 6, find the general solution of the given system of equations. Also draw a direction field and a phase portrait. Describe how the solutions behave as t→ ∞0.arrow_forward1. L, V4- x²dx.arrow_forward18. If the number of healthy fish f varies as the amount a of food available, how many fish would be present when 6 Ibs. of food are available? (Assume that 120 fish corresponds to 8 Ibs. of food.)arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
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
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
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
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman