**Frequency Distribution and Probability**A frequency distribution is shown below. Complete parts (a) and (b). **The number of televisions per household in a small town**| Televisions | Households ||-------------|------------|| 0 | 29 || 1 | 445 || 2 | 730 || 3 | 1405 |### (a) Use the frequency distribution to construct a probability distribution.To construct the probability distribution, divide the number of households for each category by the total number of households. Let’s calculate the probabilities for each category:- Total households = 29 + 445 + 730 + 1405 = 2609| x (Televisions) | P(x) (Probability) ||-----------------|-------------------|| 0 | 29/2609 ≈ 0.011 || 1 | 445/2609 ≈ 0.171 || 2 | 730/2609 ≈ 0.280 || 3 | 1405/2609 ≈ 0.539 |### (b) Graph the probability distribution using a histogram.When graphing the probability distribution, we use a histogram where the x-axis represents the number of televisions, and the y-axis represents the probability P(x).**Graph Options:**- **Option A:** This histogram represents an increasing trend but doesn’t match the computed probabilities.- **Option B:** This histogram starts low and increases in probability, matching the expected distribution based on calculations.- **Option C:** This histogram shows a decreasing trend, opposite to our data.**Correct Graph:** Option B is correct, as it accurately represents the increasing numbers (0.011, 0.171, 0.280, 0.539) matching the computed probability distribution.

Answered: Image /qna-images/answer/17b0c64e-c573-4dc3-a859-7fb53e2b18c2.jpg

A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions 1 3 Households 29 445 730 1405 (a) Use the frequency distribution to construct a probability distribution. P(x) 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. OB. Oc. AP(x) 0.6- 0.5- 0.4- 0.3- AP(x) 0.6- 0.5- 0.4- AP(x) 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- 0.3- 0.2- 0.2- 0.1- 0.1-

A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions 1 3 Households 29 445 730 1405 (a) Use the frequency distribution to construct a probability distribution. P(x) 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. OB. Oc. AP(x) 0.6- 0.5- 0.4- 0.3- AP(x) 0.6- 0.5- 0.4- AP(x) 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- 0.3- 0.2- 0.2- 0.1- 0.1-

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**

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

**The number of televisions per household in a small town**

| Televisions | Households |
|-------------|------------|
| 0 | 29 |
| 1 | 445 |
| 2 | 730 |
| 3 | 1405 |

### (a) Use the frequency distribution to construct a probability distribution.

To construct the probability distribution, divide the number of households for each category by the total number of households.

Let’s calculate the probabilities for each category:

- Total households = 29 + 445 + 730 + 1405 = 2609

| x (Televisions) | P(x) (Probability) |
|-----------------|-------------------|
| 0 | 29/2609 ≈ 0.011 |
| 1 | 445/2609 ≈ 0.171 |
| 2 | 730/2609 ≈ 0.280 |
| 3 | 1405/2609 ≈ 0.539 |

### (b) Graph the probability distribution using a histogram.

When graphing the probability distribution, we use a histogram where the x-axis represents the number of televisions, and the y-axis represents the probability P(x).

**Graph Options:**

- **Option A:** This histogram represents an increasing trend but doesn’t match the computed probabilities.
- **Option B:** This histogram starts low and increases in probability, matching the expected distribution based on calculations.
- **Option C:** This histogram shows a decreasing trend, opposite to our data.

**Correct Graph:** Option B is correct, as it accurately represents the increasing numbers (0.011, 0.171, 0.280, 0.539) matching the computed probability distribution.

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