question 16

find the area to the left of $z = 1.65$.

* 0.9505
* 0.9495

Question

question 16

find the area to the left of $z = 1.65$.

* 0.9505
* 0.9495

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 Table" ], "new_concepts": [], "current_concepts": [ "Standard Normal Table", "Z-score Calculation", "Interval Probability" ] } ## Identify the given value and target We need to find the cumulative area under the standard normal curve to the left of a given z-score: $$ Z = 1.65 $$ ## Find the cumulative probability Using the *Standard Normal Table* knowledge point $$ P(Z < 1.65) = \Phi(1.65) = 0.9505 $$

0.9505

0.9495

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.exp(-x*x/2) / Math.sqrt(2*Math.PI)", "latex": "\frac{1}{\sqrt{2\pi}} e^{-\frac{z^2}{2}}" }, -4, 4 ], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "name": "f(z)", "withLabel": false } }, { "type": "inequality", "params": [ { "x_val": 1.65, "latex": "z \le 1.65" }, [0, 0.1] ], "properties": { "isVertical": true, "inverse": false, "strict": false, "fillColor": "rgba(140, 85, 242, 0.3)", "strokeColor": "#8C55F2", "strokeWidth": 1 } }, { "type": "line", "params": [ [1.65, -1], [1.65, 1] ], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "dash": 2, "name": "z = 1.65", "withLabel": true, "labelPosition": [1.8, 0.2] } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Standard Normal Table" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given value and target

Find the cumulative probability

Answer: