at least 99.75% of the data in any data set lie within how many standard deviations of the mean? explain how you arrived at your answer.

explain how the number of standard deviations could be found for any data set. choose the correct answer below.

a. use chebychevs theorem.
b. use the empirical rule.
c. use the coefficient of variation.

find the number of standard deviations.
(k = \) (round to the nearest integer as needed.)

Question

at least 99.75% of the data in any data set lie within how many standard deviations of the mean? explain how you arrived at your answer.

explain how the number of standard deviations could be found for any data set. choose the correct answer below.

a. use chebychevs theorem.
b. use the empirical rule.
c. use the coefficient of variation.

find the number of standard deviations.
(k = \)   (round to the nearest integer as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Chebyshevs Theorem" ], "new_concepts": [], "current_concepts": [ "Chebyshevs Theorem", "Empirical Rule Percentiles" ] } ## Identify the appropriate statistical rule Using the *Chebyshevs Theorem* knowledge point $$ 1 - \frac{1}{k^2} \ge 0.9975 $$ ## Solve for the number of standard deviations Using the *Chebyshevs Theorem* knowledge point $$ \begin{aligned} \frac{1}{k^2} &\le 1 - 0.9975 \ \frac{1}{k^2} &\le 0.0025 \ k^2 &\ge \frac{1}{0.0025} \ k^2 &\ge 400 \ k &\ge 20 \end{aligned} $$ ## Question 1 A. Use Chebychev's Theorem.

B. Use the Empirical Rule.

C. Use the Coefficient of Variation. ## Question 2 $k =$ 20 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Chebyshevs Theorem" ] }

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Question

Explanation:

Identify the appropriate statistical rule

Solve for the number of standard deviations

Answer:

Question 1

Question 2