Math Problem Statement

also the options for the distribution of x is skewed to the left, right or symmetrical

Solution

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Math Problem Analysis

Mathematical Concepts

Exponential Distribution
Probability
Percentiles
Skewness
Mean
Standard Deviation

Formulas

Mean of exponential distribution: E(X) = β
Standard deviation of exponential distribution: SD(X) = β
CDF of exponential distribution: P(X ≤ x) = 1 - e^(-x / β)
Percentile formula: X_p = -β * ln(1 - p)
Complement rule for probability: P(X > x) = 1 - P(X ≤ x)

Theorems

Properties of the Exponential Distribution

Suitable Grade Level

Grades 11-12