A frequency distribution is shown below. Complete pants (a) and (b). The number of televisions per household in a small town Televisions 0 1 2 3 Households 26 440 725 1402 (a) Use the frequency distribution to construct a probability distribution. P(x) X 0 1 2 3 (Round to three decimal places as needed.) (b) Graph the probability distribution using a histogram. Choose the correct graph of the distribution below. OA. AP(x) 0.6- 0.5- 0.4- 0.3- 0.2 0.1- # of Televisions OB. AP(x) *** 0.6 0.5- 0.4- 0.3- 0.2 0.1- # of Televisions ON O C. AP(x) 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- # of Televisions Q Next C O Oc
A frequency distribution is shown below. Complete pants (a) and (b). The number of televisions per household in a small town Televisions 0 1 2 3 Households 26 440 725 1402 (a) Use the frequency distribution to construct a probability distribution. P(x) X 0 1 2 3 (Round to three decimal places as needed.) (b) Graph the probability distribution using a histogram. Choose the correct graph of the distribution below. OA. AP(x) 0.6- 0.5- 0.4- 0.3- 0.2 0.1- # of Televisions OB. AP(x) *** 0.6 0.5- 0.4- 0.3- 0.2 0.1- # of Televisions ON O C. AP(x) 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- # of Televisions Q Next C O Oc
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
![**Transcription and Explanation for Educational Website**
---
The table and exercise shown here are part of a statistics problem focusing on the distribution of televisions in households within a small town. Below is a detailed explanation.
---
**The Number of Televisions per Household in a Small Town:**
| Televisions | Households |
|-------------|------------|
| 0 | 26 |
| 1 | 440 |
| 2 | 725 |
| 3 | 1402 |
---
### Task (a)
**Construct a Probability Distribution:**
To construct the probability distribution, calculate the probability \( P(x) \) for each value \( x \) (number of televisions), based on the frequency of households:
1. **Determine Total Households:** Sum up the households:
\[
26 + 440 + 725 + 1402 = 2593
\]
2. **Calculate Probability for Each \( x \):**
\[
P(0) = \frac{26}{2593}
\]
\[
P(1) = \frac{440}{2593}
\]
\[
P(2) = \frac{725}{2593}
\]
\[
P(3) = \frac{1402}{2593}
\]
3. **Probability Values Rounded to Three Decimal Places:**
- \( P(0) = 0.010 \)
- \( P(1) = 0.170 \)
- \( P(2) = 0.280 \)
- \( P(3) = 0.541 \)
---
### Task (b)
**Graph the Probability Distribution Using a Histogram:**
Below are three histogram options labeled A, B, and C. Each shows different distributions. Choose the correct one based on the calculated probabilities.
- **Explanation of Histogram Options:**
- **Option A:** Bars incorrectly distributed.
- **Option B:** Correct distribution (matches calculated probabilities of \( P(x) \)).
- **Option C:** Bars incorrectly distributed.
**Conclusion:** Option B is the correct histogram that represents the calculated probability distribution of televisions per household.
---
This concludes the explanation. Practice constructing probability distributions and interpreting graphical representations such as histograms to enhance your statistical analysis skills.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d4c8cb-af63-459c-8cdf-c777fdfe530a%2F85df8edf-f7d6-4c7b-94a4-6c2a0394af67%2Fke7avad_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Website**
---
The table and exercise shown here are part of a statistics problem focusing on the distribution of televisions in households within a small town. Below is a detailed explanation.
---
**The Number of Televisions per Household in a Small Town:**
| Televisions | Households |
|-------------|------------|
| 0 | 26 |
| 1 | 440 |
| 2 | 725 |
| 3 | 1402 |
---
### Task (a)
**Construct a Probability Distribution:**
To construct the probability distribution, calculate the probability \( P(x) \) for each value \( x \) (number of televisions), based on the frequency of households:
1. **Determine Total Households:** Sum up the households:
\[
26 + 440 + 725 + 1402 = 2593
\]
2. **Calculate Probability for Each \( x \):**
\[
P(0) = \frac{26}{2593}
\]
\[
P(1) = \frac{440}{2593}
\]
\[
P(2) = \frac{725}{2593}
\]
\[
P(3) = \frac{1402}{2593}
\]
3. **Probability Values Rounded to Three Decimal Places:**
- \( P(0) = 0.010 \)
- \( P(1) = 0.170 \)
- \( P(2) = 0.280 \)
- \( P(3) = 0.541 \)
---
### Task (b)
**Graph the Probability Distribution Using a Histogram:**
Below are three histogram options labeled A, B, and C. Each shows different distributions. Choose the correct one based on the calculated probabilities.
- **Explanation of Histogram Options:**
- **Option A:** Bars incorrectly distributed.
- **Option B:** Correct distribution (matches calculated probabilities of \( P(x) \)).
- **Option C:** Bars incorrectly distributed.
**Conclusion:** Option B is the correct histogram that represents the calculated probability distribution of televisions per household.
---
This concludes the explanation. Practice constructing probability distributions and interpreting graphical representations such as histograms to enhance your statistical analysis skills.
Expert Solution
Step 1
Data given
| X | 0 | 1 | 2 | 3 |
| Frequency | 26 | 440 | 725 | 1402 |
Step by step
Solved in 3 steps
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