Math Problem Statement
After 8:00pm on each Thursday, the amount of time that a person spends waiting in line to get into a well-known pub is a random variable represented by X. Suppose we can model the behavior of X with the exponential probability distribution with an average waiting time of 42 minutes.
55% of the time, you will have to wait at most how many minutes to get into this pub? Enter your answer to two decimals.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Exponential Distribution
Cumulative Distribution Function (CDF)
Formulas
Exponential PDF: f(x) = λe^{-λx}, x ≥ 0
CDF of Exponential Distribution: F(x) = 1 - e^{-λx}
λ = 1/mean (where mean = 42 minutes)
Theorems
Exponential Distribution Properties
Memorylessness of Exponential Distribution
Suitable Grade Level
Grades 11-12 or College-Level Statistics
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