Mechanical Engineering Exam > Mechanical Engineering Questions > A bus arrives every 10 minutes at a bus stop....
Start Learning for Free
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes is
- a)0.1
- b)0.7
- c)0.2
- d)0.3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X ...
P (7< <10) = 
= 0.3
= 0.3 Hint p.d.f is f(x) = 
Most Upvoted Answer
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X ...
P (7< <10) = = 0.3
= 0.3 Hint p.d.f is f(x) =
Free Test
FREE
| Start Free Test |
Community Answer
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X ...
Question Analysis
The question states that a bus arrives every 10 minutes at a bus stop. The waiting time for the bus, denoted as X, is assumed to be uniformly distributed. We are asked to find the probability that a person has to wait for the bus for more than 7 minutes.
Solution
To solve this problem, we need to understand the concept of a uniform distribution and apply it to find the probability.
Uniform Distribution
In statistics, a uniform distribution is a probability distribution in which all outcomes are equally likely. In this case, the waiting time for the bus is assumed to follow a uniform distribution because the bus arrives every 10 minutes, and there is an equal likelihood of the bus arriving at any given minute within that 10-minute interval.
Finding the Probability
To find the probability that a person has to wait for the bus for more than 7 minutes, we need to calculate the area under the probability density function (PDF) curve for the waiting time X, from 7 minutes to 10 minutes.
Since the waiting time X is uniformly distributed, the PDF is a constant within the interval [0, 10] and zero outside that interval. The height of the PDF is 1/10, as the total area under the curve must be equal to 1.
Calculating the Probability
To calculate the probability, we need to find the area under the PDF curve from 7 minutes to 10 minutes. This can be done by finding the length of the interval [7, 10] and multiplying it by the height of the PDF.
Length of Interval = 10 - 7 = 3 minutes
Height of PDF = 1/10
Area under Curve = Length of Interval * Height of PDF
Area under Curve = 3 * (1/10) = 3/10
Therefore, the probability that a person has to wait for the bus for more than 7 minutes is 3/10 or 0.3.
Answer
The correct answer is option D) 0.3.
The question states that a bus arrives every 10 minutes at a bus stop. The waiting time for the bus, denoted as X, is assumed to be uniformly distributed. We are asked to find the probability that a person has to wait for the bus for more than 7 minutes.
Solution
To solve this problem, we need to understand the concept of a uniform distribution and apply it to find the probability.
Uniform Distribution
In statistics, a uniform distribution is a probability distribution in which all outcomes are equally likely. In this case, the waiting time for the bus is assumed to follow a uniform distribution because the bus arrives every 10 minutes, and there is an equal likelihood of the bus arriving at any given minute within that 10-minute interval.
Finding the Probability
To find the probability that a person has to wait for the bus for more than 7 minutes, we need to calculate the area under the probability density function (PDF) curve for the waiting time X, from 7 minutes to 10 minutes.
Since the waiting time X is uniformly distributed, the PDF is a constant within the interval [0, 10] and zero outside that interval. The height of the PDF is 1/10, as the total area under the curve must be equal to 1.
Calculating the Probability
To calculate the probability, we need to find the area under the PDF curve from 7 minutes to 10 minutes. This can be done by finding the length of the interval [7, 10] and multiplying it by the height of the PDF.
Length of Interval = 10 - 7 = 3 minutes
Height of PDF = 1/10
Area under Curve = Length of Interval * Height of PDF
Area under Curve = 3 * (1/10) = 3/10
Therefore, the probability that a person has to wait for the bus for more than 7 minutes is 3/10 or 0.3.
Answer
The correct answer is option D) 0.3.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer?
Question Description
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer?.
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer?.
Solutions for A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. 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 bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes isa)0.1b)0.7c) 0.2d)0.3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup