Math Problem Statement

The graph of a uniform probability distribution is given below. If necessary, round results accurate to at least 3 decimal places.

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a. What is the probability density function (e.g., what is the height of the line that is the graph of the distribution)?

f(x)=   

b. Find the mean of the distribution.

μ=   

c. Find the standard deviation of the distribution.

σ=   

d. Find the probability represented by the shaded region.    

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Statistics
Uniform Distribution

Formulas

f(x) = 1 / (b - a)
μ = (a + b) / 2
σ = (b - a) / sqrt(12)
P(c ≤ x ≤ d) = (d - c) / (b - a)

Theorems

Uniform Distribution Properties
Standard Deviation Formula
Mean Formula

Suitable Grade Level

College Level (Probability and Statistics)