use the standard normal table to find the specified area.

between one standard deviation above the mean and three standard deviations above the mean.

click here to view page 1 of the standard normal table.
click here to view page 2 of the standard normal table.

the area that lies between one standard deviation above the mean and three standard deviations above the mean is .
(round to four decimal places as needed.)

Question

use the standard normal table to find the specified area.

between one standard deviation above the mean and three standard deviations above the mean.

click here to view page 1 of the standard normal table.
click here to view page 2 of the standard normal table.

the area that lies between one standard deviation above the mean and three standard deviations above the mean is  .
(round to four decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Standard Normal Table", "Normal Distribution" ], "new_concepts": [], "current_concepts": [ "Standard Normal Table", "Normal Distribution", "Z-score Definition" ] } ## Identify the standard normal boundary values Using the *Normal Distribution* knowledge point $$ \begin{aligned} z_1 &= 1.00 \ z_2 &= 3.00 \end{aligned} $$ ## Find cumulative areas from the standard normal table Using the *Standard Normal Table* knowledge point $$ \begin{aligned} P(Z < 3.00) &= 0.9987 \ P(Z < 1.00) &= 0.8413 \end{aligned} $$ ## Calculate the area between the boundaries Using the *Normal Distribution* knowledge point $$ \begin{aligned} P(1.00 < Z < 3.00) &= P(Z < 3.00) - P(Z < 1.00) \ &= 0.9987 - 0.8413 \ &= 0.1574 \end{aligned} $$ The area that lies between one standard deviation above the mean and three standard deviations above the mean is 0.1574. { "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.exp(-x*x/2) / Math.sqrt(2*Math.PI)", "latex": "\frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}" }, -4, 4 ], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "name": "f(z)", "withLabel": false } }, { "type": "inequality", "params": [ { "js": "Math.exp(-x*x/2) / Math.sqrt(2*Math.PI)", "latex": "y \le f(z)" }, [2, 0.05] ], "properties": { "inverse": false, "strict": false, "fillColor": "rgba(140, 85, 242, 0.3)", "strokeColor": "none" } }, { "type": "inequality", "params": [ { "x_val": 1, "latex": "z \ge 1" }, [1.5, 0.1] ], "properties": { "isVertical": true, "inverse": true, "strict": false, "strokeColor": "#8C55F2", "strokeWidth": 1 } }, { "type": "inequality", "params": [ { "x_val": 3, "latex": "z \le 3" }, [2.5, 0.1] ], "properties": { "isVertical": true, "inverse": false, "strict": false, "strokeColor": "#8C55F2", "strokeWidth": 1 } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Standard Normal Table" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard normal boundary values

Find cumulative areas from the standard normal table

Calculate the area between the boundaries

Answer: