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**Probability Distribution of Dogs Per Household in a Small Town** The following data represents the probability distribution of the number of dogs per household in a small town: | Dogs | 0 | 1 | 2 | 3 | 4 | 5 | |------|-------|-------|-------|-------|-------|-------| | Probability | 0.667 | 0.204 | 0.084 | 0.025 | 0.014 | 0.006 | **Tasks:** **(a) Find the mean, variance, and standard deviation of the probability distribution.** - **Mean (μ):** Calculate the mean of the probability distribution and round to one decimal place as needed. - **Variance (σ²):** Calculate the variance of the probability distribution and round to one decimal place as needed. - **Standard Deviation (σ):** Calculate the standard deviation of the probability distribution and round to one decimal place as needed. **(b) Interpret the results in the context of the real-life situation.** **Options:** A. A household on average has 0.5 dog with a standard deviation of 11 dogs. B. A household on average has 0.9 dog with a standard deviation of 0.5 dog. C. A household on average has 0.5 dog with a standard deviation of 0.9 dog. D. A household on average has 0.8 dog with a standard deviation of 0.9 dog. *Please perform the calculations based on the given probability distribution to select the correct interpretation.* --- **Additional Information:** The lower portion of the image contains unrelated order and reservation details from a separate context, which are not relevant to the educational content of this exercise.

**Probability Distribution of Dogs Per Household in a Small Town** The following data represents the probability distribution of the number of dogs per household in a small town: | Dogs | 0 | 1 | 2 | 3 | 4 | 5 | |------|-------|-------|-------|-------|-------|-------| | Probability | 0.667 | 0.204 | 0.084 | 0.025 | 0.014 | 0.006 | **Tasks:** **(a) Find the mean, variance, and standard deviation of the probability distribution.** - **Mean (μ):** Calculate the mean of the probability distribution and round to one decimal place as needed. - **Variance (σ²):** Calculate the variance of the probability distribution and round to one decimal place as needed. - **Standard Deviation (σ):** Calculate the standard deviation of the probability distribution and round to one decimal place as needed. **(b) Interpret the results in the context of the real-life situation.** **Options:** A. A household on average has 0.5 dog with a standard deviation of 11 dogs. B. A household on average has 0.9 dog with a standard deviation of 0.5 dog. C. A household on average has 0.5 dog with a standard deviation of 0.9 dog. D. A household on average has 0.8 dog with a standard deviation of 0.9 dog. *Please perform the calculations based on the given probability distribution to select the correct interpretation.* --- **Additional Information:** The lower portion of the image contains unrelated order and reservation details from a separate context, which are not relevant to the educational content of this exercise.

MATLAB: An Introduction with Applications
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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**Probability Distribution of Dogs Per Household in a Small Town** The following data represents the probability distribution of the number of dogs per household in a small town: | Dogs | 0 | 1 | 2 | 3 | 4 | 5 | |------|-------|-------|-------|-------|-------|-------| | Probability | 0.667 | 0.204 | 0.084 | 0.025 | 0.014 | 0.006 | **Tasks:** **(a) Find the mean, variance, and standard deviation of the probability distribution.** - **Mean (μ):** Calculate the mean of the probability distribution and round to one decimal place as needed. - **Variance (σ²):** Calculate the variance of the probability distribution and round to one decimal place as needed. - **Standard Deviation (σ):** Calculate the standard deviation of the probability distribution and round to one decimal place as needed. **(b) Interpret the results in the context of the real-life situation.** **Options:** A. A household on average has 0.5 dog with a standard deviation of 11 dogs. B. A household on average has 0.9 dog with a standard deviation of 0.5 dog. C. A household on average has 0.5 dog with a standard deviation of 0.9 dog. D. A household on average has 0.8 dog with a standard deviation of 0.9 dog. *Please perform the calculations based on the given probability distribution to select the correct interpretation.* --- **Additional Information:** The lower portion of the image contains unrelated order and reservation details from a separate context, which are not relevant to the educational content of this exercise.
Transcribed Image Text:**Probability Distribution of Dogs Per Household in a Small Town** The following data represents the probability distribution of the number of dogs per household in a small town: | Dogs | 0 | 1 | 2 | 3 | 4 | 5 | |------|-------|-------|-------|-------|-------|-------| | Probability | 0.667 | 0.204 | 0.084 | 0.025 | 0.014 | 0.006 | **Tasks:** **(a) Find the mean, variance, and standard deviation of the probability distribution.** - **Mean (μ):** Calculate the mean of the probability distribution and round to one decimal place as needed. - **Variance (σ²):** Calculate the variance of the probability distribution and round to one decimal place as needed. - **Standard Deviation (σ):** Calculate the standard deviation of the probability distribution and round to one decimal place as needed. **(b) Interpret the results in the context of the real-life situation.** **Options:** A. A household on average has 0.5 dog with a standard deviation of 11 dogs. B. A household on average has 0.9 dog with a standard deviation of 0.5 dog. C. A household on average has 0.5 dog with a standard deviation of 0.9 dog. D. A household on average has 0.8 dog with a standard deviation of 0.9 dog. *Please perform the calculations based on the given probability distribution to select the correct interpretation.* --- **Additional Information:** The lower portion of the image contains unrelated order and reservation details from a separate context, which are not relevant to the educational content of this exercise.
Expert Solution
Step 1

Given that 

Probability mass function of X is 

Dogs=X 0 1 2 3 4 5
P(Dogs=X) 0.667 0.204 0.084 0.025 0.014 0.006
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