mean temperature: 78°
standard deviation: 5°

check all of the temperatures that are within one standard deviation of the mean.
- 72°
- 74°
- 79°
- 84°

Question

mean temperature: 78°
standard deviation: 5°

check all of the temperatures that are within one standard deviation of the mean.
- 72°
- 74°
- 79°
- 84°

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": [ "Basic Statistics" ], "new_concepts": [ "Standard Deviation Interval" ], "current_concepts": [ "Basic Statistics", "Standard Deviation Interval" ] } ## Identify the given statistical parameters Using the *Basic Statistics* knowledge point $$ \begin{aligned} &\text{Mean } (\mu) = 78^\circ\ &\text{Standard deviation } (\sigma) = 5^\circ \end{aligned} $$ ## Calculate the interval within one standard deviation Using the *Basic Statistics* knowledge point $$ \begin{aligned} &\text{Lower Bound} = \mu - \sigma = 78 - 5 = 73^\circ\ &\text{Upper Bound} = \mu + \sigma = 78 + 5 = 83^\circ\ &\text{Interval} = [73^\circ, 83^\circ] \end{aligned} $$ ## Evaluate the given temperature options Using the *Basic Statistics* knowledge point $$ \begin{aligned} &72^\circ: 72 < 73 \quad (\text{Outside})\ &74^\circ: 73 \le 74 \le 83 \quad (\text{Within})\ &79^\circ: 73 \le 79 \le 83 \quad (\text{Within})\ &84^\circ: 84 > 83 \quad (\text{Outside}) \end{aligned} $$

72°

74°

79°

84°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Standard Deviation Interval" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given statistical parameters

Calculate the interval within one standard deviation

Evaluate the given temperature options

Answer: