Math Problem Statement

At a certain bus stop, the length of time needed to wait for the next bus is known to follow an Exponential probability distribution where the mean is 1.6 hours. Let X be the time (in hours) that a randomly-selected passenger needed to wait for the next bus.

Then find the probability that it was between 330 and 435 minutes, rounded to 3 places.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Exponential Distribution
Cumulative Distribution Function (CDF)

Formulas

Rate parameter: λ = 1 / μ
CDF of Exponential Distribution: F(x) = 1 - e^(-λx)

Theorems

Exponential Distribution Theorem

Suitable Grade Level

Grades 11-12