the mean of a set of credit scores is $\mu = 690$ and $\sigma = 14$. which credit score is within a z-score of 3.3?

634
640
720
750

Question

the mean of a set of credit scores is $\mu = 690$ and $\sigma = 14$. which credit score is within a z-score of 3.3?

634
640
720
750

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", "Population Mean Symbol", "Population Standard Deviation" ] } ## Define the given parameters Using the *Z-Score Formula* knowledge point $$ \begin{aligned} \mu &= 690 \ \sigma &= 14 \ |z| &\le 3.3 \end{aligned} $$ ## Calculate the boundary values Using the *Z-Score Formula* knowledge point $$ \begin{aligned} x_{\text{min}} &= \mu - 3.3\sigma = 690 - 3.3(14) = 690 - 46.2 = 643.8 \ x_{\text{max}} &= \mu + 3.3\sigma = 690 + 3.3(14) = 690 + 46.2 = 736.2 \end{aligned} $$ ## Determine the valid credit score Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &\text{Interval: } [643.8, 736.2] \ &634 < 643.8 \quad (\text{Outside}) \ &640 < 643.8 \quad (\text{Outside}) \ &643.8 \le 720 \le 736.2 \quad (\text{Within}) \ &750 > 736.2 \quad (\text{Outside}) \end{aligned} $$

(A) 634

(B) 640

(C) 720

(D) 750

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

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QUESTION IMAGE

Question

Explanation:

Define the given parameters

Calculate the boundary values

Determine the valid credit score

Answer: