find the probability that z lies between -1.2 and 0.

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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": [ "Standard Normal Distribution", "Interval Probability" ], "new_concepts": [], "current_concepts": [ "Standard Normal Distribution", "Interval Probability" ] } ## Define the probability expression Using the *Standard Normal Distribution* knowledge point $$ P(-1.2 < z < 0) $$ ## Apply symmetry properties Using the *Standard Normal Distribution* and *Interval Probability* knowledge points $$ P(-1.2 < z < 0) = P(0 < z < 1.2) = P(z < 1.2) - P(z < 0) $$ ## Evaluate using standard normal values Using the *Standard Normal Distribution* knowledge point $$ \begin{aligned} P(z < 1.2) &= 0.8849 \ P(z < 0) &= 0.5000 \ P(-1.2 < z < 0) &= 0.8849 - 0.5000 = 0.3849 \end{aligned} $$

(A) 0.3849

(B) 0.3869

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Question

Explanation:

Define the probability expression

Apply symmetry properties

Evaluate using standard normal values

Answer: