Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > The number of cars arriving at ICICI bank dri...
Start Learning for Free
The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.
Que : The probability that more than 3 cars will arrive during any 10 min period is
- a)0.249
- b)0.143
- c)0.346
- d)0.543
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The number of cars arriving at ICICI bank drive-in window during 10-mi...
Most Upvoted Answer
The number of cars arriving at ICICI bank drive-in window during 10-mi...
Solution:
Given, the number of cars arriving at ICICI bank drive-in window during a 10-minute period is a Poisson random variable X with parameter λ = 2.
To find the probability that more than 3 cars will arrive during any 10-minute period, we need to calculate P(X > 3).
Step 1: Find the probability of having 0, 1, 2, and 3 cars
- The probability mass function of a Poisson random variable is given by P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of cars.
- Using the parameter λ = 2, we can calculate the probabilities for 0, 1, 2, and 3 cars:
- P(X = 0) = (e^(-2) * 2^0) / 0! = e^(-2) ≈ 0.1353
- P(X = 1) = (e^(-2) * 2^1) / 1! = 2e^(-2) ≈ 0.2707
- P(X = 2) = (e^(-2) * 2^2) / 2! = 2e^(-2) ≈ 0.2707
- P(X = 3) = (e^(-2) * 2^3) / 3! = (8e^(-2))/6 ≈ 0.1805
Step 2: Calculate the probability of having more than 3 cars
- To find P(X > 3), we need to sum the probabilities of having 4, 5, 6, and so on, up to infinity.
- P(X > 3) = 1 - P(X ≤ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
≈ 1 - (0.1353 + 0.2707 + 0.2707 + 0.1805)
≈ 1 - 0.8572
≈ 0.1428
Therefore, the probability that more than 3 cars will arrive during any 10-minute period is approximately 0.1428, which is closest to option B (0.143).
Hence, the correct answer is option B.
Given, the number of cars arriving at ICICI bank drive-in window during a 10-minute period is a Poisson random variable X with parameter λ = 2.
To find the probability that more than 3 cars will arrive during any 10-minute period, we need to calculate P(X > 3).
Step 1: Find the probability of having 0, 1, 2, and 3 cars
- The probability mass function of a Poisson random variable is given by P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of cars.
- Using the parameter λ = 2, we can calculate the probabilities for 0, 1, 2, and 3 cars:
- P(X = 0) = (e^(-2) * 2^0) / 0! = e^(-2) ≈ 0.1353
- P(X = 1) = (e^(-2) * 2^1) / 1! = 2e^(-2) ≈ 0.2707
- P(X = 2) = (e^(-2) * 2^2) / 2! = 2e^(-2) ≈ 0.2707
- P(X = 3) = (e^(-2) * 2^3) / 3! = (8e^(-2))/6 ≈ 0.1805
Step 2: Calculate the probability of having more than 3 cars
- To find P(X > 3), we need to sum the probabilities of having 4, 5, 6, and so on, up to infinity.
- P(X > 3) = 1 - P(X ≤ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
≈ 1 - (0.1353 + 0.2707 + 0.2707 + 0.1805)
≈ 1 - 0.8572
≈ 0.1428
Therefore, the probability that more than 3 cars will arrive during any 10-minute period is approximately 0.1428, which is closest to option B (0.143).
Hence, the correct answer is option B.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer?
Question Description
The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer?.
The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer?.
Solutions for The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.Que : The probability that more than 3 cars will arrive during any 10 min period isa)0.249b)0.143c)0.346d)0.543Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) 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.
x
![]()
For Your Perfect Score in Electronics and Communication Engineering (ECE)
The Best you need at One Place
|
© 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