Math Problem Statement

On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 15 minutes. What is the probability of a waiting time in excess of 25 minutes between successive speeders?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Exponential Distribution

Formulas

Probability Density Function (PDF) for Exponential Distribution: f(t) = λe^(-λt), t ≥ 0
Rate Parameter: λ = 1 / mean
Cumulative Distribution Function (CDF): P(T ≤ t) = 1 - e^(-λt)
Complementary Probability: P(T > t) = e^(-λt)

Theorems

Exponential Distribution Theorem
Memorylessness of Exponential Distribution

Suitable Grade Level

Grades 11-12 or Introductory College Level