a missing data value from a set of data has a z-score of $-2.1$. fred already calculated the mean and standard deviation to be $\mu = 43$ and $\sigma = 2$. what was the missing data value? round the answer to the nearest whole number.

39
41
45
47

Question

a missing data value from a set of data has a z-score of \$-2.1\$. fred already calculated the mean and standard deviation to be \$\mu = 43\$ and \$\sigma = 2\$. what was the missing data value? round the answer to the nearest whole number.

39
41
45
47

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" ] } ## Identify the given values and formula Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z = -2.1\ &\mu = 43\ &\sigma = 2\ &z = \frac{x - \mu}{\sigma} \end{aligned} $$ ## Set up the equation for the missing value Using the *Z-Score Formula* knowledge point $$ -2.1 = \frac{x - 43}{2} $$ ## Solve for the missing data value Using the *Z-Score Formula* knowledge point $$ \begin{aligned} x - 43 &= -2.1 \cdot 2\ x - 43 &= -4.2\ x &= 43 - 4.2\ x &= 38.8 \end{aligned} $$ ## Round to the nearest whole number Using the *Z-Score Formula* knowledge point $$ x \approx 39 $$

(A) 39

(B) 41

(C) 45

(D) 47

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Set up the equation for the missing value

Solve for the missing data value

Round to the nearest whole number

Answer: