Mechanical Engineering Exam > Mechanical Engineering Questions > The arrival of customers over fixed time inte...
Start Learning for Free
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).
Correct answer is '0.383'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The arrival of customers over fixed time intervals in a bank follow a ...
Most Upvoted Answer
The arrival of customers over fixed time intervals in a bank follow a ...
Given:
- The arrival of customers follows a Poisson distribution.
- Average number of customers per hour is 30.
To find:
- The probability that the time between successive customer arrivals is between 1 and 3 minutes.
Solution:
Step 1: Calculation of Arrival Rate
- The average number of customers per hour is given as 30.
- We need to convert this to the arrival rate λ (lambda) which is the average number of customers per time unit.
- There are 60 minutes in an hour, so the arrival rate λ (lambda) can be calculated as:
λ = (30 customers/hour) / (60 minutes/hour) = 0.5 customers/minute
Step 2: Calculation of Probability
- The time between successive customer arrivals follows an exponential distribution.
- The mean of the exponential distribution is equal to the inverse of the arrival rate (λ).
Mean = 1 / λ = 1 / 0.5 = 2 minutes
- We need to find the probability that the time between successive customer arrivals is between 1 and 3 minutes.
- This can be calculated using the cumulative distribution function (CDF) of the exponential distribution.
- The CDF of the exponential distribution is given by:
CDF(x) = 1 - e^(-λx)
- To find the probability of the time between successive customer arrivals being between 1 and 3 minutes, we can calculate the difference between the CDF values at x=3 and x=1.
- Probability = CDF(3) - CDF(1)
= 1 - e^(-λ*3) - (1 - e^(-λ*1))
= e^(-λ) - e^(-3λ)
Step 3: Calculation of Probability
- Substitute the value of λ into the equation to calculate the probability.
λ = 0.5 customers/minute
- Probability = e^(-0.5) - e^(-3*0.5)
= e^(-0.5) - e^(-1.5)
≈ 0.6065306597 - 0.2231301601
≈ 0.383
Answer:
The probability that the time between successive customer arrivals is between 1 and 3 minutes is approximately 0.383.
- The arrival of customers follows a Poisson distribution.
- Average number of customers per hour is 30.
To find:
- The probability that the time between successive customer arrivals is between 1 and 3 minutes.
Solution:
Step 1: Calculation of Arrival Rate
- The average number of customers per hour is given as 30.
- We need to convert this to the arrival rate λ (lambda) which is the average number of customers per time unit.
- There are 60 minutes in an hour, so the arrival rate λ (lambda) can be calculated as:
λ = (30 customers/hour) / (60 minutes/hour) = 0.5 customers/minute
Step 2: Calculation of Probability
- The time between successive customer arrivals follows an exponential distribution.
- The mean of the exponential distribution is equal to the inverse of the arrival rate (λ).
Mean = 1 / λ = 1 / 0.5 = 2 minutes
- We need to find the probability that the time between successive customer arrivals is between 1 and 3 minutes.
- This can be calculated using the cumulative distribution function (CDF) of the exponential distribution.
- The CDF of the exponential distribution is given by:
CDF(x) = 1 - e^(-λx)
- To find the probability of the time between successive customer arrivals being between 1 and 3 minutes, we can calculate the difference between the CDF values at x=3 and x=1.
- Probability = CDF(3) - CDF(1)
= 1 - e^(-λ*3) - (1 - e^(-λ*1))
= e^(-λ) - e^(-3λ)
Step 3: Calculation of Probability
- Substitute the value of λ into the equation to calculate the probability.
λ = 0.5 customers/minute
- Probability = e^(-0.5) - e^(-3*0.5)
= e^(-0.5) - e^(-1.5)
≈ 0.6065306597 - 0.2231301601
≈ 0.383
Answer:
The probability that the time between successive customer arrivals is between 1 and 3 minutes is approximately 0.383.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer?
Question Description
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer?.
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer?.
Solutions for The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer?, a detailed solution for The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? has been provided alongside types of The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).Correct answer is '0.383'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup