ols A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 1 2 3 4 0 P(X=x) 0.0857 0.2447 0.3208 0.2415 0.1073 wwwww www. www.IV www.viv (Round to four decimal places as needed.) OA. The mean number of girls in a family is B. The mean number of girls in a family with four children is 2.0400. C. The mean number of children in a family with four girls is b. Obtain the standard deviation of the random variable. o=1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. O D. O C. O A. OB. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 04- 0.5- 0.4- 05 04- 0.3 0.14 001234 001234 01234 01234 Help me solve this View an example Get more help. 0.5 0.4- 0.3+ 0.24 0.1- "A S 14 Clear all Check answer
ols A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 1 2 3 4 0 P(X=x) 0.0857 0.2447 0.3208 0.2415 0.1073 wwwww www. www.IV www.viv (Round to four decimal places as needed.) OA. The mean number of girls in a family is B. The mean number of girls in a family with four children is 2.0400. C. The mean number of children in a family with four girls is b. Obtain the standard deviation of the random variable. o=1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. O D. O C. O A. OB. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 04- 0.5- 0.4- 05 04- 0.3 0.14 001234 001234 01234 01234 Help me solve this View an example Get more help. 0.5 0.4- 0.3+ 0.24 0.1- "A S 14 Clear all Check answer
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:### Statistical Analysis and Probability Distributions: Understanding Binomial Distribution
---
#### Problem Context:
A survey was conducted in a town where each family had four children. The objective is to understand the distribution of the number of girls in these families.
#### Given Data:
- **Random Variable \(X\)**: Number of girls born to a randomly selected couple in a town with four children.
- The probability distribution for the random variable \(X\) is given, representing the number of girls (0, 1, 2, 3, or 4).
| \( X \) | P( \( X = x \) ) |
|--------|------------------|
| 0 | 0.0625 |
| 1 | 0.2500 |
| 2 | 0.3750 |
| 3 | 0.2500 |
| 4 | 0.0625 |
#### Tasks:
1. **Calculate the Mean**:
- The mean number of girls in the family is \( 2.0 \).
2. **Calculate the Standard Deviation**:
- The standard deviation for the number of girls is \( 1.00 \).
3. **Probability Histogram**:
- You are provided with four histogram options to visually represent the probability distribution of the random variable \(X\).
---
#### Detailed Description of Histogram Options:
- **Option A**:
- Probability values are represented on the vertical axis.
- Number of girls is represented on the horizontal axis (from 0 to 4).
- The heights of the bars correspond to the probabilities 0.0625, 0.2500, 0.3750, 0.2500, and 0.0625 respectively from 0 to 4.
- **Option B**:
- Similar to Option A but with an incorrect probability representation.
- **Option C**:
- Similar to Option A but with an incorrect probability representation.
- **Option D**:
- Similar to Option A but with an incorrect probability representation.
---
#### Correct Histogram Selection:
- The correct histogram should reflect the probabilities 0.0625, 0.2500, 0.3750, 0.2500, and 0.0625 for the values 0, 1, 2, 3
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