Question

Do interruptions while you are working reduce your productivity? According to a University of California-Irvine study, businesspeople are interrupted at the rate of approximately $5^{1 / 2}$ times per hour (Fortune, March 20,2006 ). Suppose the number of interruptions follows a Poisson probability distribution. a. Show the probability distribution for the time between interruptions. b. What is the probability a businessperson will have no interruptions during a 15 -minute period? c. What is the probability that the next interruption will occur within 10 minutes for a particular businessperson?

Name: Problem 38, Chapter 6: Essential of Statistics for Business and Economics
Uploaded: 2022-02-05T01:40:29-08:00
Duration: 4 min 11 s
Channel: Michael Nartey

   Do interruptions while you are working reduce your productivity? According to a University of California-Irvine study, businesspeople are interrupted at the rate of approximately $5^{1 / 2}$ times per hour (Fortune, March 20,2006 ). Suppose the number of interruptions follows a Poisson probability distribution.
a. Show the probability distribution for the time between interruptions.
b. What is the probability a businessperson will have no interruptions during a 15 -minute period?
c. What is the probability that the next interruption will occur within 10 minutes for a particular businessperson?

Essential of Statistics for Business and Economics

David R. Anderson,… 5th Edition

Chapter 6, Problem 38

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Solved by Expert Michael Nartey

02/05/2022

Step 1

- We are given that interruptions follow a Poisson distribution with a rate of $ \lambda = 5^{1/2} $ interruptions per hour. - We need to find the probability distribution for the time between interruptions, which follows an exponential distribution with rate \( Show more…

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Do interruptions while you are working reduce your productivity? According to a University of California-Irvine study, businesspeople are interrupted at the rate of approximately $5^{1 / 2}$ times per hour (Fortune, March 20,2006 ). Suppose the number of interruptions follows a Poisson probability distribution. a. Show the probability distribution for the time between interruptions. b. What is the probability a businessperson will have no interruptions during a 15 -minute period? c. What is the probability that the next interruption will occur within 10 minutes for a particular businessperson?

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Key Concepts

Poisson Process

A Poisson process is a statistical model used to describe events that occur independently and randomly in time or space at a constant average rate. It is widely used for modeling counts of events and forms the basis for both the Poisson and exponential distributions.

Rate Parameter

The rate parameter, often denoted by lambda (?), represents the average number of events occurring per unit time in a Poisson process. It is a crucial parameter as it directly influences the probabilities calculated in both Poisson and exponential distributions.

Exponential Distribution

The exponential distribution models the time between events in a Poisson process. It is characterized by a constant rate of occurrence and the memoryless property, which means that the probability of an event occurring in the future is independent of how much time has already elapsed.

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