the set of life spans of an appliance is normally distributed with a mean $\mu = 48$ months and a standard deviation $\sigma = 8$ months. what is the life span of an appliance that has a z-score of $-3$?

3 months
24 months
45 months
72 months

Question

the set of life spans of an appliance is normally distributed with a mean \$\mu = 48\$ months and a standard deviation \$\sigma = 8\$ months. what is the life span of an appliance that has a z-score of \$-3\$?

3 months
24 months
45 months
72 months

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": [ "Z-Score Formula" ], "new_concepts": [], "current_concepts": [ "Z-Score Formula", "Normal Distribution" ] } ## Identify the given parameters Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &\mu = 48\ &\sigma = 8\ &z = -3 \end{aligned} $$ ## Solve for the life span Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z = \frac{x - \mu}{\sigma}\ &-3 = \frac{x - 48}{8}\ &x - 48 = -24\ &x = 24 \end{aligned} $$

(A) 3 months

(B) 24 months

(C) 45 months

(D) 72 months

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Z-Score Formula" ] }

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Question

Explanation:

Identify the given parameters

Solve for the life span

Answer: