MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**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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Transcribed Image Text:**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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