Math Problem Statement

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. Standardized Test Composite Scores 26 6 32 Score mu equals 19.9sigma equals 5.426 less than x less than 32 x

A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 39 with tick marks at 6, 26, and 32. A normal curve labeled μ = 19.9 σ = 5.4 is centered above the x-axis at 19.9. Two vertical line segments extend from the curve to the x-axis at 26 and 32. The area below the curve and between the two vertical line segments is shaded and labeled 26 < x < 32. Question content area bottom Part 1 The probability that the member selected at random is from the shaded area of the graph is    enter your response here. ​(Round to four decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Normal Distribution
Z-Scores

Formulas

z = (x - μ) / σ
P(a < x < b) = P(z_b) - P(z_a)

Theorems

Standard Normal Distribution

Suitable Grade Level

Grades 10-12