mean temperature: $78^\circ$
standard deviation: $5^\circ$

check all of the temperatures that are within one standard deviation of the mean.
x $72^\circ$
v $74^\circ$
v $79^\circ$
x $84^\circ$

how many years had temperatures that were exactly one standard deviation from the mean?

Question

mean temperature: $78^\circ$
standard deviation: $5^\circ$

check all of the temperatures that are within one standard deviation of the mean.
x $72^\circ$
v $74^\circ$
v $79^\circ$
x $84^\circ$

how many years had temperatures that were exactly one standard deviation from the mean?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Standard Deviation Interval" ], "new_concepts": [], "current_concepts": [ "Standard Deviation Interval", "Graph Interpretation" ] } ## Calculate the target temperatures Using the *Standard Deviation Interval* knowledge point $$ \begin{aligned} &\mu = 78^\circ\ &\sigma = 5^\circ\ &\text{Exactly one standard deviation from the mean} = \mu \pm \sigma\ &78^\circ - 5^\circ = 73^\circ\ &78^\circ + 5^\circ = 83^\circ \end{aligned} $$ ## Count the occurrences from the dot plot Using the *Standard Deviation Interval* knowledge point $$ \begin{aligned} &\text{Number of dots at } 73^\circ = 2\ &\text{Number of dots at } 83^\circ = 2\ &\text{Total years} = 2 + 2 = 4 \end{aligned} $$ How many years had temperatures that were exactly one standard deviation from the mean? 4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Standard Deviation Interval" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the target temperatures

Count the occurrences from the dot plot

Answer: