the mean score on a statistics exam is 60 points, with a standard deviation of 4 points. apply chebychevs theorem to the data using k = 2. interpret the results.

at least $\square$% of the exam scores fall between $\square$ and $\square$.
(simplify your answers.)

Question

the mean score on a statistics exam is 60 points, with a standard deviation of 4 points. apply chebychevs theorem to the data using k = 2. interpret the results.

at least $\square$% of the exam scores fall between $\square$ and $\square$.
(simplify your answers.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Chebyshev's Theorem" ], "current_concepts": [ "Chebyshev's Theorem", "Mean and Standard Deviation" ] } ## Calculate the minimum percentage using Chebyshev's Theorem $$ 1 - \frac{1}{k^2} = 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = 0.75 = 75\% $$ ## Calculate the lower and upper bounds of the interval $$ \begin{aligned} \text{Lower Bound} &= \mu - k\sigma = 60 - 2(4) = 52 \ \text{Upper Bound} &= \mu + k\sigma = 60 + 2(4) = 68 \end{aligned} $$ At least 75% of the exam scores fall between 52 and 68. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Chebyshev's Theorem" ] }

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Explanation:

Calculate the minimum percentage using Chebyshev's Theorem

Calculate the lower and upper bounds of the interval

Answer: