A factory use predictive maintenance to monitor the performance and condition of operation tools during regular operation to reduce the likelihood of failures. From the analysis, the number of operation tools failures in a day follows a Poisson distribution with an average of 1.25 failures. On a particular day, the stock keeper reported that there were only five replacement tools in stock. A new delivery of replacements tools will only arrive after four days. If all five replacement tools are used before the new delivery arrives, a further replacement cannot be done until the delivery arrives. (i) Determine the probability that three replacements of operation tools are required over the next four days. (ii) Determine the expected number of replacements made over the next four days. (You must show all of the details of your calculations)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

This is an easy question 

A factory use predictive maintenance to monitor the performance and condition of operation tools
during regular operation to reduce the likelihood of failures. From the analysis, the number of
operation tools failures in a day follows a Poisson distribution with an average of 1.25 failures. On
a particular day, the stock keeper reported that there were only five replacement tools in stock. A
new delivery of replacements tools will only arrive after four days. If all five replacement tools are
used before the new delivery arrives, a further replacement cannot be done until the delivery arrives.
(i) Determine the probability that three replacements of operation tools are required over the next
four days.
(ii) Determine the expected number of replacements made over the next four days. (You must show
all of the details of your calculations)
Transcribed Image Text:A factory use predictive maintenance to monitor the performance and condition of operation tools during regular operation to reduce the likelihood of failures. From the analysis, the number of operation tools failures in a day follows a Poisson distribution with an average of 1.25 failures. On a particular day, the stock keeper reported that there were only five replacement tools in stock. A new delivery of replacements tools will only arrive after four days. If all five replacement tools are used before the new delivery arrives, a further replacement cannot be done until the delivery arrives. (i) Determine the probability that three replacements of operation tools are required over the next four days. (ii) Determine the expected number of replacements made over the next four days. (You must show all of the details of your calculations)
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman