use the information in the table to answer the question.

what percentage of goldfish will have lengths between 4.6 inches and 9.4 inches?

34%
68%
95%
99.7%

Question

use the information in the table to answer the question.

what percentage of goldfish will have lengths between 4.6 inches and 9.4 inches?

34%
68%
95%
99.7%

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": [ "Normal Distribution", "Standard Deviation Interval", "Z-Score Formula" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Standard Deviation Interval", "Z-Score Formula", "Empirical Rule" ] } ## Identify given parameters Using the *Normal Distribution* knowledge point $$ \begin{aligned} \mu &= 7 \ \sigma &= 1.2 \end{aligned} $$ ## Calculate Z-scores for the boundaries Using the *Z-Score Formula* knowledge point $$ \begin{aligned} z_1 &= \frac{4.6 - 7}{1.2} = \frac{-2.4}{1.2} = -2 \ z_2 &= \frac{9.4 - 7}{1.2} = \frac{2.4}{1.2} = 2 \end{aligned} $$ ## Apply the Empirical Rule Using the *Standard Deviation Interval* knowledge point $$ \begin{aligned} P(-2 \le Z \le 2) \approx 95\% \end{aligned} $$

34%

68%

95%

99.7%

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Normal Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given parameters

Calculate Z-scores for the boundaries

Apply the Empirical Rule

Answer: