complete parts (a) and (b) below.
the number of dogs per household in a small town
$\begin{array}{lcccccc}
\text{dogs} & 0 & 1 & 2 & 3 & 4 & 5 \\
\text{probability} & 0.676 & 0.203 & 0.078 & 0.023 & 0.012 & 0.007
\end{array}$

(a) find the mean, variance, and standard deviation of the probability distribution.
find the mean of the probability distribution.
$\mu = 0.5$ (round to one decimal place as needed.)

find the variance of the probability distribution.
$\sigma^2 = 0.8$ (round to one decimal place as needed.)

find the standard deviation of the probability distribution.
$\sigma = 0.9$ (round to one decimal place as needed.)

(b) interpret the results in the context of the real-life situation.

a. a household on average has 0.8 dog with a standard deviation of 0.9 dog.
b. a household on average has 0.5 dog with a standard deviation of 0.9 dog.
c. a household on average has 0.5 dog with a standard deviation of 16 dogs.
d. a household on average has 0.9 dog with a standard deviation of 0.5 dog.

Question

complete parts (a) and (b) below.
the number of dogs per household in a small town
$\begin{array}{lcccccc}
\text{dogs} & 0 & 1 & 2 & 3 & 4 & 5 \\
\text{probability} & 0.676 & 0.203 & 0.078 & 0.023 & 0.012 & 0.007
\end{array}$

(a) find the mean, variance, and standard deviation of the probability distribution.
find the mean of the probability distribution.
$\mu = 0.5$ (round to one decimal place as needed.)

find the variance of the probability distribution.
$\sigma^2 = 0.8$ (round to one decimal place as needed.)

find the standard deviation of the probability distribution.
$\sigma = 0.9$ (round to one decimal place as needed.)

(b) interpret the results in the context of the real-life situation.

a. a household on average has 0.8 dog with a standard deviation of 0.9 dog.
b. a household on average has 0.5 dog with a standard deviation of 0.9 dog.
c. a household on average has 0.5 dog with a standard deviation of 16 dogs.
d. a household on average has 0.9 dog with a standard deviation of 0.5 dog.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Discrete Probability Distribution", "Mean of Probability Distribution", "Variance of Probability Distribution" ] } ## Identify the calculated parameters $$ \begin{aligned} &\mu = 0.5\ &\sigma^2 = 0.8\ &\sigma = 0.9 \end{aligned} $$ ## Match parameters to interpretation statements $$ \begin{aligned} &\text{Average (Mean) } \mu = 0.5 \text{ dog}\ &\text{Standard Deviation } \sigma = 0.9 \text{ dog} \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &\text{Option A: Average } 0.8\text{, SD } 0.9 \quad (\text{Incorrect})\ &\text{Option B: Average } 0.5\text{, SD } 0.9 \quad (\text{Correct})\ &\text{Option C: Average } 0.5\text{, SD } 16 \quad (\text{Incorrect})\ &\text{Option D: Average } 0.9\text{, SD } 0.5 \quad (\text{Incorrect}) \end{aligned} $$

A. A household on average has 0.8 dog with a standard deviation of 0.9 dog.

B. A household on average has 0.5 dog with a standard deviation of 0.9 dog.

C. A household on average has 0.5 dog with a standard deviation of 16 dogs.

D. A household on average has 0.9 dog with a standard deviation of 0.5 dog.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Discrete Probability Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the calculated parameters

Match parameters to interpretation statements

Evaluate the given options

Answer: