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Q. The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?
- a)162
- b)180
- c)201
- d)190
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Q.The number of accidents in a year attributed to taxi drivers in a lo...
Given:
- Number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2.
- 500 taxi drivers in that area.
To find: The number of drivers with at least 3 accidents in a year.
Solution:
- Let X be the number of accidents in a year by a taxi driver.
- Then, X follows a Poisson distribution with parameter λ=2.
- The probability of a taxi driver having at least 3 accidents in a year can be represented as P(X≥3).
- Using the complement rule, we can write P(X≥3) = 1 - P(X<3) =="" 1="" -="" [p(x="0)" +="" p(x="1)" +="" p(x="">
- We know that the probability mass function of Poisson distribution is given by P(X=k) = (e^(-λ)*λ^k) / k!, where k is a non-negative integer.
- Using this formula, we can calculate the probabilities P(X=0), P(X=1), and P(X=2) as follows:
P(X=0) = (e^(-2)*2^0) / 0! = e^(-2)
P(X=1) = (e^(-2)*2^1) / 1! = 2e^(-2)
P(X=2) = (e^(-2)*2^2) / 2! = 2e^(-2)
- Substituting these values in the above formula, we get:
P(X≥3) = 1 - [e^(-2) + 2e^(-2) + 2e^(-2)] = 1 - 5e^(-2) ≈ 0.3233
- The number of drivers with at least 3 accidents in a year can be obtained by multiplying the above probability by the total number of taxi drivers (500):
Number of drivers with at least 3 accidents = 0.3233 * 500 ≈ 161.65
- Round off to the nearest integer, we get 162.
Therefore, the number of drivers with at least 3 accidents in a year is 162. Hence, option (a) is the correct answer.
- Number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2.
- 500 taxi drivers in that area.
To find: The number of drivers with at least 3 accidents in a year.
Solution:
- Let X be the number of accidents in a year by a taxi driver.
- Then, X follows a Poisson distribution with parameter λ=2.
- The probability of a taxi driver having at least 3 accidents in a year can be represented as P(X≥3).
- Using the complement rule, we can write P(X≥3) = 1 - P(X<3) =="" 1="" -="" [p(x="0)" +="" p(x="1)" +="" p(x="">
- We know that the probability mass function of Poisson distribution is given by P(X=k) = (e^(-λ)*λ^k) / k!, where k is a non-negative integer.
- Using this formula, we can calculate the probabilities P(X=0), P(X=1), and P(X=2) as follows:
P(X=0) = (e^(-2)*2^0) / 0! = e^(-2)
P(X=1) = (e^(-2)*2^1) / 1! = 2e^(-2)
P(X=2) = (e^(-2)*2^2) / 2! = 2e^(-2)
- Substituting these values in the above formula, we get:
P(X≥3) = 1 - [e^(-2) + 2e^(-2) + 2e^(-2)] = 1 - 5e^(-2) ≈ 0.3233
- The number of drivers with at least 3 accidents in a year can be obtained by multiplying the above probability by the total number of taxi drivers (500):
Number of drivers with at least 3 accidents = 0.3233 * 500 ≈ 161.65
- Round off to the nearest integer, we get 162.
Therefore, the number of drivers with at least 3 accidents in a year is 162. Hence, option (a) is the correct answer.
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Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer?
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Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer?.
Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer?.
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Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Q.The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with an average 2. Out of 500 taxi drivers of that area, what is the number of drivers with at least 3 accidents in a year?a)162b)180c)201d)190Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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