use the standard normal table to find the specified area.

between one standard deviation below the mean and one standard deviation above the mean.

link to page 1 of the standard normal table
link to page 2 of the standard normal table

the area between one standard deviation below the mean and one standard deviation 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 below the mean and one standard deviation above the mean.

link to page 1 of the standard normal table
link to page 2 of the standard normal table

the area between one standard deviation below the mean and one standard deviation 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", "quick" ], "needs_drawing": false, "concepts_used": [ "Standard Normal Distribution", "Z-Score Table" ], "new_concepts": [], "current_concepts": [ "Standard Normal Distribution", "Z-Score Table", "Empirical Rule" ] } ## Identify the z-scores for the boundaries $$ \begin{aligned} z_1 &= -1.00 \ z_2 &= 1.00 \end{aligned} $$ ## Find cumulative areas from the standard normal table $$ \begin{aligned} P(Z < 1.00) &= 0.8413 \ P(Z < -1.00) &= 0.1587 \end{aligned} $$ ## Calculate the area between the boundaries $$ \begin{aligned} P(-1.00 < Z < 1.00) &= P(Z < 1.00) - P(Z < -1.00) \ &= 0.8413 - 0.1587 \ &= 0.6826 \end{aligned} $$ The area between one standard deviation below the mean and one standard deviation above the mean is 0.6826. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Standard Normal Distribution" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the z-scores for the boundaries

Find cumulative areas from the standard normal table

Calculate the area between the boundaries

Answer: