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 z-score of an appliance that stopped working at 64 months?

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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 z-score of an appliance that stopped working at 64 months?

-2
-1
1
2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Z-Score Formula" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Z-Score Formula" ] } ## Identify the given parameters $$ \mu = 48,\quad \sigma = 8,\quad x = 64 $$ ## Apply the z-score formula $$ z = \frac{x - \mu}{\sigma} $$ ## Calculate the final value $$ z = \frac{64 - 48}{8} = \frac{16}{8} = 2 $$

(A) $-2$

(B) $-1$

(C) $1$

(D) $2$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the z-score formula

Calculate the final value

Answer: