type the correct answer in the box. use numerals instead of words.

the mean of a normally distributed dataset is 12, and the standard deviation is 2.

% of the data points lie between 8 and 16.

Question

type the correct answer in the box. use numerals instead of words.

the mean of a normally distributed dataset is 12, and the standard deviation is 2.

% of the data points lie between 8 and 16.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Empirical Rule" ], "new_concepts": [], "current_concepts": [ "Empirical Rule", "Normal Distribution Calculations" ] } ## Calculate the z-scores for the boundaries $$ \begin{aligned} &\mu = 12,\quad \sigma = 2\ &z_1 = \frac{8 - 12}{2} = -2\ &z_2 = \frac{16 - 12}{2} = 2 \end{aligned} $$ ## Apply the Empirical Rule $$ \begin{aligned} &P(-2 \le Z \le 2) = 0.95\ &\text{Percentage} = 95\% \end{aligned} $$ Type the correct answer in the box. Use numerals instead of words. The mean of a normally distributed dataset is 12, and the standard deviation is 2. 95 % of the data points lie between 8 and 16. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Empirical Rule" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the z-scores for the boundaries

Apply the Empirical Rule

Answer: