use the probability distribution to complete parts (a) and (b) below.

the number of school-related extracurricular activities per student
activities: 0, 1, 2, 3, 4, 5, 6, 7
probability: 0.059, 0.122, 0.162, 0.179, 0.214, 0.127, 0.086, 0.051

(a) find the mean, variance, and standard deviation of the probability distribution.

the mean is .
(round to one decimal place as needed.)

Question

use the probability distribution to complete parts (a) and (b) below.

the number of school-related extracurricular activities per student
activities: 0, 1, 2, 3, 4, 5, 6, 7
probability: 0.059, 0.122, 0.162, 0.179, 0.214, 0.127, 0.086, 0.051

(a) find the mean, variance, and standard deviation of the probability distribution.

the mean is  .
(round to one decimal place as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mean of Probability Distribution" ], "new_concepts": [], "current_concepts": [ "Discrete Probability Distribution", "Mean of Probability Distribution" ] } ## Calculate the expected value (mean) of the discrete random variable $$ \begin{aligned} \mu = \sum x \cdot P(x) &= 0(0.059) + 1(0.122) + 2(0.162) + 3(0.179) + 4(0.214) + 5(0.127) + 6(0.086) + 7(0.051) \ &= 0 + 0.122 + 0.324 + 0.537 + 0.856 + 0.635 + 0.516 + 0.357 \ &= 3.347 \end{aligned} $$ ## Round the calculated mean to one decimal place $$ \mu \approx 3.3 $$ The mean is 3.3. (Round to one decimal place as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Mean of Probability Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the expected value (mean) of the discrete random variable

Round the calculated mean to one decimal place

Answer: