Mechanical Engineering Exam  >  Mechanical Engineering Questions  >   A garage is manned with a single worker. Cus... Start Learning for Free
A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________
  • a)
    1.9
  • b)
    2.2
Correct answer is between ' 1.9, 2.2'. Can you explain this answer?
Verified Answer
A garage is manned with a single worker. Customers arrive at a rate o...
λ = 20/hour
= 2.08 minutes
View all questions of this test
Most Upvoted Answer
A garage is manned with a single worker. Customers arrive at a rate o...
λ = 20/hour
= 2.08 minutes
Free Test
Community Answer
A garage is manned with a single worker. Customers arrive at a rate o...
Given information:
- Customers arrive at a rate of 20 per hour.
- The time required to provide service is exponentially distributed with a mean of 100 seconds.

Calculating the arrival rate:
- The arrival rate can be calculated by dividing the number of customers arriving per hour by the number of minutes in an hour.
- In this case, the arrival rate is 20 customers per hour, which is equivalent to 20/60 = 1/3.33 customers per minute.

Calculating the service rate:
- The service rate can be calculated by taking the reciprocal of the mean service time.
- In this case, the mean service time is 100 seconds, which is equivalent to 100/60 = 5/3 minutes.
- Therefore, the service rate is 1/(5/3) = 3/5 customers per minute.

Calculating the mean waiting time:
- The mean waiting time can be calculated using the formula: mean waiting time = 1/(service rate - arrival rate)
- In this case, the arrival rate is 1/3.33 customers per minute and the service rate is 3/5 customers per minute.
- Substituting the values into the formula, we get: mean waiting time = 1/((3/5) - (1/3.33))

Simplifying the expression:
- To simplify the expression, we need to find a common denominator for the denominators.
- The common denominator is (3.33 x 5) = 16.65.
- Rewriting the expression with the common denominator, we get: mean waiting time = 1/((9.99/16.65) - (5/16.65))

Calculating the mean waiting time:
- Simplifying the expression further, we get: mean waiting time = 1/(4.99/16.65)
- Dividing 1 by (4.99/16.65), we get: mean waiting time = 16.65/4.99
- Evaluating the expression, we get: mean waiting time = 3.33 minutes

Conclusion:
- The mean waiting time for a customer needing repair facility in the queue is approximately 3.33 minutes, which is between 1.9 and 2.2 minutes.
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 Engineering

A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer?
Question Description
A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. 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 A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. 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 A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer?.
Solutions for A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. 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 A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer?, a detailed solution for A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer? has been provided alongside types of A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A garage is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 100 seconds. The mean waiting time (in minutes) of a customer, needing repair facility in the queue will be __________a) 1.9b) 2.2Correct answer is between ' 1.9, 2.2'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev