**Using Probability Distributions and Histograms: An Example of Household Sizes**This educational section focuses on analyzing a probability distribution using a histogram. The goal is to determine the mean, variance, standard deviation, and expected value, and then interpret the results. We will examine the distribution of household sizes in Country A for a recent year.### Histogram ExplanationThe histogram displays household sizes (1 through 6) on the x-axis and the probability (P(x)) of each size on the y-axis. Each bar represents a household size and its corresponding probability:- Size 1: Probability = 0.286- Size 2: Probability = 0.322- Size 3: Probability = 0.149- Size 4: Probability = 0.152- Size 5: Probability = 0.059- Size 6: Probability = 0.032### CalculationsTo better understand the distribution, complete the following:(a) **The mean is** ___. *(Type an integer or a decimal. Do not round.)*(b) **The variance is** ___. *(Round to two decimal places as needed.)*(c) **The standard deviation is** ___. *(Round to two decimal places as needed.)*(d) **The expected value is** ___. *(Type an integer or a decimal. Do not round.)*### InterpretationChoose all applicable interpretations based on your results:- **A.** Most household sizes differ from the expected value by 1 or 2 people.- **B.** The average household is expected to have either 2 or 3 people.- **C.** The average household is expected to have either 1 or 2 people.- **D.** Most household sizes differ from the expected value by 2 or 3 people.To engage further, select your answer(s) based on your interpretation of the data.

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Use the probability distribution or histogram to find the (a) mean, (b) variance, (c) standard deviation, and (d) expected value of the probability distribution, and (e) interpret the results. The histogram shows the distribution of household sizes in country A for a recent year. AP(x) 0.40- 0.322 0.286 0.30- 0.20- 0.149 0.152 0.10- 0.059 0.032 0.00- Household Size (a) The mean is (Type an integer or a decimal. Do not round.) (b) The variance is. (Round to two decimal places as needed.) (c) The standard deviation is. (Round to two decimal places as needed.)

Use the probability distribution or histogram to find the (a) mean, (b) variance, (c) standard deviation, and (d) expected value of the probability distribution, and (e) interpret the results. The histogram shows the distribution of household sizes in country A for a recent year. AP(x) 0.40- 0.322 0.286 0.30- 0.20- 0.149 0.152 0.10- 0.059 0.032 0.00- Household Size (a) The mean is (Type an integer or a decimal. Do not round.) (b) The variance is. (Round to two decimal places as needed.) (c) The standard deviation is. (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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

**Using Probability Distributions and Histograms: An Example of Household Sizes**

This educational section focuses on analyzing a probability distribution using a histogram. The goal is to determine the mean, variance, standard deviation, and expected value, and then interpret the results. We will examine the distribution of household sizes in Country A for a recent year.

### Histogram Explanation
The histogram displays household sizes (1 through 6) on the x-axis and the probability (P(x)) of each size on the y-axis. Each bar represents a household size and its corresponding probability:

- Size 1: Probability = 0.286
- Size 2: Probability = 0.322
- Size 3: Probability = 0.149
- Size 4: Probability = 0.152
- Size 5: Probability = 0.059
- Size 6: Probability = 0.032

### Calculations
To better understand the distribution, complete the following:

(a) **The mean is** ___.
*(Type an integer or a decimal. Do not round.)*

(b) **The variance is** ___.
*(Round to two decimal places as needed.)*

(c) **The standard deviation is** ___.
*(Round to two decimal places as needed.)*

(d) **The expected value is** ___.
*(Type an integer or a decimal. Do not round.)*

### Interpretation
Choose all applicable interpretations based on your results:

- **A.** Most household sizes differ from the expected value by 1 or 2 people.
- **B.** The average household is expected to have either 2 or 3 people.
- **C.** The average household is expected to have either 1 or 2 people.
- **D.** Most household sizes differ from the expected value by 2 or 3 people.

To engage further, select your answer(s) based on your interpretation of the data.

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