question 1 points 3
if $x$ follows a normal distribution with $\mu = 108$ and $\sigma = 12$, what is the probability that $96

Question

question 1 points 3
if $x$ follows a normal distribution with $\mu = 108$ and $\sigma = 12$, what is the probability that $96 < x < 120$?

13.84%
68.26%

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Normal Distribution Properties" ], "new_concepts": [ "Empirical Rule", "Z-score Calculation" ], "current_concepts": [ "Normal Distribution Properties", "Empirical Rule", "Z-score Calculation" ] } ## Identify parameters Using the *Normal Distribution Properties* knowledge point $$ \mu = 108,\quad \sigma = 12 $$ ## Calculate Z-scores Using the *Normal Distribution Properties* knowledge point $$ \begin{aligned} Z_1 &= \frac{96 - 108}{12} = -1\ Z_2 &= \frac{120 - 108}{12} = 1 \end{aligned} $$ ## Find the probability Using the *Normal Distribution Properties* knowledge point $$ P(-1 < Z < 1) \approx 0.6826 = 68.26\% $$

(A) 13.84%

(B) 68.26%

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QUESTION IMAGE

Question

Explanation:

Identify parameters

Calculate Z-scores

Find the probability

Answer: