Question

Times to gather preliminary information from arrivals at an outpatient clinic follow an exponential distribution with mean 15 minutes. Find the probability, for a randomly chosen arrival, that more than 18 minutes will be required.

Name: Problem 56, Chapter 5: Statistics for Business and Economics
Uploaded: 2022-01-07T20:24:42-08:00
Duration: 1 min 41 s
Channel: Christopher Stanley
Description: Times to gather preliminary information from arrivals at an outpatient clinic follow an exponential distribution with mean 15 minutes. Find the probability, for a randomly chosen arrival, that more than 18 minutes will be required.

   Times to gather preliminary information from arrivals at an outpatient clinic follow an exponential distribution with mean 15 minutes. Find the probability, for a randomly chosen arrival, that more than 18 minutes will be required.

Statistics for Business and Economics

Paul Newbold,… 8th Edition

Chapter 5, Problem 56

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Solved by Expert Christopher Stanley

01/07/2022

Step 1

This means that the rate parameter $\lambda$ is $\frac{1}{15}$. Show more…

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Times to gather preliminary information from arrivals at an outpatient clinic follow an exponential distribution with mean 15 minutes. Find the probability, for a randomly chosen arrival, that more than 18 minutes will be required.

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Key Concepts

Exponential Distribution

The exponential distribution is a continuous probability distribution that is often used to model the time between independent events that occur at a constant average rate. It is characterized by its memoryless property, meaning that the probability of an event occurring in the future is independent of the past.

Rate Parameter and Mean Relationship

In the exponential distribution, the mean (or expected value) is the reciprocal of the rate parameter, denoted by lambda. This relationship, expressed as mean = 1/lambda, allows the conversion from the given average time between events to the rate at which the events occur.

Survival Function

The survival function for the exponential distribution, defined as P(X > x) = exp(-lambda * x), gives the probability that the event of interest takes longer than a specified time. This function is crucial when calculating the probability of events exceeding a certain duration.

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