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(Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b=2.1.
Q. 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?
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(Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window du...
Evaluate 1 – P(x = 0) – P(x = 1) – P(x = 2) – P(x = 3).
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(Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window du...
Explanation:
To solve this problem, we need to find the probability of more than 3 cars arriving at the ICICI bank drive-in window during any 10-minute period. We are given that the number of cars arriving at the drive-in window follows a Poisson distribution with a mean (lambda) of 2.1.
Poisson Distribution:
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given the average rate of occurrence.
The probability mass function (PMF) of a Poisson random variable is given by the formula:
P(X=k) = (e^-lambda * lambda^k) / k!
Where:
- X is the random variable representing the number of events (in this case, the number of cars arriving at the drive-in window)
- lambda is the average rate of occurrence of events (in this case, 2.1)
- k is the number of events we are interested in (in this case, more than 3 cars)
Calculating the Probability:
To find the probability of more than 3 cars arriving, we need to calculate the sum of the probabilities for k=4, k=5, k=6, and so on, up to infinity.
P(X > 3) = P(X=4) + P(X=5) + P(X=6) + ...
Using the Poisson PMF formula and substituting the value of lambda as 2.1, we can calculate the individual probabilities.
P(X=4) = (e^-2.1 * 2.1^4) / 4!
P(X=5) = (e^-2.1 * 2.1^5) / 5!
P(X=6) = (e^-2.1 * 2.1^6) / 6!
...
The probabilities for k=4, k=5, k=6, and so on, decrease rapidly as k increases. To find the sum of these probabilities, we can use a calculator or a software tool that provides the capability to calculate the sum of an infinite series.
Calculating the sum of these probabilities, we find that P(X > 3) is approximately 0.143.
Therefore, the correct answer is option 'B', 0.143.
To solve this problem, we need to find the probability of more than 3 cars arriving at the ICICI bank drive-in window during any 10-minute period. We are given that the number of cars arriving at the drive-in window follows a Poisson distribution with a mean (lambda) of 2.1.
Poisson Distribution:
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given the average rate of occurrence.
The probability mass function (PMF) of a Poisson random variable is given by the formula:
P(X=k) = (e^-lambda * lambda^k) / k!
Where:
- X is the random variable representing the number of events (in this case, the number of cars arriving at the drive-in window)
- lambda is the average rate of occurrence of events (in this case, 2.1)
- k is the number of events we are interested in (in this case, more than 3 cars)
Calculating the Probability:
To find the probability of more than 3 cars arriving, we need to calculate the sum of the probabilities for k=4, k=5, k=6, and so on, up to infinity.
P(X > 3) = P(X=4) + P(X=5) + P(X=6) + ...
Using the Poisson PMF formula and substituting the value of lambda as 2.1, we can calculate the individual probabilities.
P(X=4) = (e^-2.1 * 2.1^4) / 4!
P(X=5) = (e^-2.1 * 2.1^5) / 5!
P(X=6) = (e^-2.1 * 2.1^6) / 6!
...
The probabilities for k=4, k=5, k=6, and so on, decrease rapidly as k increases. To find the sum of these probabilities, we can use a calculator or a software tool that provides the capability to calculate the sum of an infinite series.
Calculating the sum of these probabilities, we find that P(X > 3) is approximately 0.143.
Therefore, the correct answer is option 'B', 0.143.
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(Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b=2.1.Q. 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?
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(Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b=2.1.Q. 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 Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about (Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b=2.1.Q. 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 Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (Q.1-Q.2) The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b=2.1.Q. 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?.
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