I am having a hard time trying to understand this topic. My TI-84 calculator has stopped working and I'm having to figure this out by hand. **Frequency Distribution in a Small Town**A frequency distribution is presented below for the number of televisions per household in a small town.| Televisions | Households ||-------------|------------|| 0 | 30 || 1 | 444 || 2 | 729 || 3 | 1402 |**Tasks:**(a) **Probability Table**- Probability for 2 televisions: 0.353- Probability for 3 televisions: 0.679- (Round probabilities to the nearest thousandth as needed.)(b) **Mean of the Probability Distribution**- Mean (μ) = 2.9 (Round to the nearest tenth as needed.)**Additional Calculations:**- **Variance (σ²) of the Probability Distribution:** - Calculation is required (Round to the nearest tenth as needed.)- **Standard Deviation (σ) of the Probability Distribution:** - Calculation is required (Round to the nearest tenth as needed.)This information can help to understand the distribution and average number of televisions per household, alongside variability within the surveyed households. ### Understanding Frequency and Probability DistributionsThe following data represents the number of televisions per household in a small town:| Televisions | Households ||-------------|------------|| 0 | 30 || 1 | 444 || 2 | 729 || 3 | 1402 |#### (a) Constructing a Probability DistributionUsing the frequency distribution, we can create a probability distribution as follows:| x | P(x) ||---|-------|| 0 | 0.012 || 1 | 0.170 || 2 | 0.353 || 3 | 0.679 |*(Note: Probabilities are rounded to the nearest thousandth.)*#### (b) Calculating the Mean of the Probability DistributionTo find the mean (μ) of the probability distribution:\[ \mu = 2.9 \]*(Rounded to the nearest tenth as needed.)*#### Calculating the Variance of the Probability DistributionThe variance (σ²) is also calculated but is not visible in this image. However, it typically follows the formula for variance of a probability distribution:\[ \sigma^2 = \sum [x^2 \cdot P(x)] - \mu^2 \]### ExplanationThe data shows that most households have 3 televisions, as indicated by the largest number in the frequency table (1402 households). The probability distribution provides a view of the likelihood of each possible outcome, with the highest probability (0.679) being for 3 televisions per household. The mean gives an average of about 2.9 televisions per household.

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Answered: A frequency distribution is shown…

A frequency distribution is shown below. Complete parts (a) through (d). The number of televisions per household in a small town Televisions 0 1 2 3 Households 30 444 729 1402 2 0.353

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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