question 37 points 1

95% of the normal distribution lies within ______ standard deviation(s) of the mean.

two
one

Question

question 37 points 1

95% of the normal distribution lies within ______ standard deviation(s) of the mean.

two
one

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Empirical Rule", "Normal Distribution Properties" ], "new_concepts": [], "current_concepts": [ "Empirical Rule", "Normal Distribution Properties" ] } ## State the given problem and target The question asks for the number of standard deviations from the mean within which $95\%$ of a normal distribution lies. ## Apply the Empirical Rule Using the **Empirical Rule** and **Normal Distribution Properties** knowledge points: $$ \begin{aligned} &\text{Within } 1\sigma: \approx 68\%\ &\text{Within } 2\sigma: \approx 95\%\ &\text{Within } 3\sigma: \approx 99.7\% \end{aligned} $$ Thus, $95\%$ of the distribution lies within two standard deviations.

two

one

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Empirical Rule" ] }

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QUESTION IMAGE

Question

Explanation:

State the given problem and target

Apply the Empirical Rule

Answer: