### Frequency Distribution and Probability DistributionA frequency distribution is shown below. Complete parts (a) and (b).#### The number of televisions per household in a small town| Televisions (x) | Households ||:---------------:|:----------:|| 0 | 29 || 1 | 448 || 2 | 729 || 3 | 1406 |#### (a) Construct a Probability DistributionUsing the frequency distribution, construct a probability distribution. The probability P(x) for each value of x is calculated as the number of households with x televisions divided by the total number of households.The probabilities will be calculated as follows:- $ P(0) = \frac{29}{2612} $- $ P(1) = \frac{448}{2612} $- $ P(2) = \frac{729}{2612} $- $ P(3) = \frac{1406}{2612} $(Round to three decimal places as needed.)#### (b) Graph the Probability Distribution using a HistogramChoose the correct graph of the distribution below:- **Option A**: The values start high, decrease, then increase again. - **Option B**: The values increase incrementally from left to right. - **Option C**: The values start high and decrease steadily.#### Describe the Histogram's ShapeChoose the correct answer to describe the shape of the histogram:1. Symmetric2. Skewed Left3. Skewed RightClick to select your answer(s).---### Explanation of Graphs- **Graph A**: This histogram shows highest probability at x = 1, dips at x = 2 and rises again at x = 3, indicating a non-monotonic distribution.- **Graph B**: Probability increases steadily, the shape is uniformly increasing.- **Graph C**: Probabilities start high and decrease steadily, indicating a left-skewed distribution.Let's identify the correct histogram to go with our calculated probabilities:- For $ P(0) = 0.011 $- For $ P(1) = 0.171 $- For $ P(2) = 0.279 $- For $ P(3) = 0.539 $Thus the correct histogram from the options would

Given information: x frequency 0 29 1 448 2 729 3 1406 Total=2612 a) Probability…

A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions 2 Households 29 448 729 1406 (a) Use the frequency distribution to construct a probability distribution. P(x) 0. 1. 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. Ов.

A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions 2 Households 29 448 729 1406 (a) Use the frequency distribution to construct a probability distribution. P(x) 0. 1. 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. Ов.

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Frequency Distribution and Probability Distribution

A frequency distribution is shown below. Complete parts (a) and (b).

#### The number of televisions per household in a small town
| Televisions (x) | Households |
|:---------------:|:----------:|
| 0 | 29 |
| 1 | 448 |
| 2 | 729 |
| 3 | 1406 |

#### (a) Construct a Probability Distribution
Using the frequency distribution, construct a probability distribution. The probability P(x) for each value of x is calculated as the number of households with x televisions divided by the total number of households.

The probabilities will be calculated as follows:
- $ P(0) = \frac{29}{2612} $
- $ P(1) = \frac{448}{2612} $
- $ P(2) = \frac{729}{2612} $
- $ P(3) = \frac{1406}{2612} $

(Round to three decimal places as needed.)

#### (b) Graph the Probability Distribution using a Histogram
Choose the correct graph of the distribution below:

- **Option A**: The values start high, decrease, then increase again.
- **Option B**: The values increase incrementally from left to right.
- **Option C**: The values start high and decrease steadily.

#### Describe the Histogram's Shape
Choose the correct answer to describe the shape of the histogram:
1. Symmetric
2. Skewed Left
3. Skewed Right

Click to select your answer(s).

---

### Explanation of Graphs
- **Graph A**: This histogram shows highest probability at x = 1, dips at x = 2 and rises again at x = 3, indicating a non-monotonic distribution.
- **Graph B**: Probability increases steadily, the shape is uniformly increasing.
- **Graph C**: Probabilities start high and decrease steadily, indicating a left-skewed distribution.

Let's identify the correct histogram to go with our calculated probabilities:
- For $ P(0) = 0.011 $
- For $ P(1) = 0.171 $
- For $ P(2) = 0.279 $
- For $ P(3) = 0.539 $

Thus the correct histogram from the options would

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