Math Problem Statement
Based on an analysis of sample data, an article proposed the pdf
f(x) = 0.35e−0.35(x − 1)
when
x ≥ 1
as a model for the distribution of
X = time (sec)
spent at the median line. (Round your answers to three decimal places.)
(a) What is the probability that waiting time is at most 6 sec? More than 6 sec?
at most 6 sec
P(X ≤ 6)
=
more than 6 sec
P(X > 6)
=
(b) What is the probability that waiting time is between 4 and 7 sec?
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Exponential Distribution
Cumulative Distribution Function (CDF)
Formulas
PDF of the exponential distribution: f(x) = λe^{-λ(x - 1)}, x ≥ 1
CDF of exponential distribution: F(x) = 1 - e^{-λ(x - 1)}
P(a ≤ X ≤ b) = F(b) - F(a)
Theorems
Exponential Distribution Theorem
Suitable Grade Level
Undergraduate
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