↓ Assume each newborn baby has a probability of approximately 0.52 of being female and 0.48 of being male. For a family with four children, let X = number of children who are girls. a. Identify the three conditions that must be satisfied for X to have the 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. Which of the below are the three conditions for a binomial distribution? 1. The n trials are independent. III. The n trials are dependent. V. There are two trials. OA. III, V, and VI OB. II, III, and V C. I, IV, and VI OD. I, II, and IV b. n = 4 p= I II. Each trial has at least two possible outcomes. IV. Each trial has the same probability of a success. VI. Each trial has two possible outcomes.
↓ Assume each newborn baby has a probability of approximately 0.52 of being female and 0.48 of being male. For a family with four children, let X = number of children who are girls. a. Identify the three conditions that must be satisfied for X to have the 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. Which of the below are the three conditions for a binomial distribution? 1. The n trials are independent. III. The n trials are dependent. V. There are two trials. OA. III, V, and VI OB. II, III, and V C. I, IV, and VI OD. I, II, and IV b. n = 4 p= I II. Each trial has at least two possible outcomes. IV. Each trial has the same probability of a success. VI. Each trial has two possible outcomes.
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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf10b40a-fae6-4e8b-9b89-0711a68556bc%2Fe145f384-d5fd-4752-b2bc-841d84216a8d%2Fv0d2058_processed.jpeg&w=3840&q=75)
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.
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