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The time between accidents at a busy intersection has a Exponential distribution with mean of 0.2 months. What is the probability that the next accident will happen in less than 2 months?

The time between accidents at a busy intersection has a Exponential distribution with mean of 0.2 months. What is the probability that the next accident will happen in less than 2 months?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1p need help please
**Problem Statement** The time between accidents at a busy intersection follows an Exponential distribution with a mean of 0.2 months. What is the probability that the next accident will happen in less than 2 months? **Solution Approach** To solve this problem, we will use the properties of the Exponential distribution. The probability that an event occurs within a certain time frame can be calculated using the cumulative distribution function (CDF) of the Exponential distribution. Given the mean is 0.2 months, the rate parameter (λ) is the reciprocal of the mean: \[ λ = \frac{1}{0.2} = 5 \] The CDF of an Exponential distribution is given by: \[ P(X \leq x) = 1 - e^{-λx} \] Substituting the given values: \[ P(X \leq 2) = 1 - e^{-5 \times 2} \] By calculating, we find the probability that the next accident will happen in less than 2 months. **Note**: The text box underneath is likely meant for entering the calculated probability.
Transcribed Image Text:**Problem Statement** The time between accidents at a busy intersection follows an Exponential distribution with a mean of 0.2 months. What is the probability that the next accident will happen in less than 2 months? **Solution Approach** To solve this problem, we will use the properties of the Exponential distribution. The probability that an event occurs within a certain time frame can be calculated using the cumulative distribution function (CDF) of the Exponential distribution. Given the mean is 0.2 months, the rate parameter (λ) is the reciprocal of the mean: \[ λ = \frac{1}{0.2} = 5 \] The CDF of an Exponential distribution is given by: \[ P(X \leq x) = 1 - e^{-λx} \] Substituting the given values: \[ P(X \leq 2) = 1 - e^{-5 \times 2} \] By calculating, we find the probability that the next accident will happen in less than 2 months. **Note**: The text box underneath is likely meant for entering the calculated probability.
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