CA Foundation Exam > CA Foundation Questions > A renowned hospital usually admits 200 patien...
Start Learning for Free
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?
?
?
Most Upvoted Answer
A renowned hospital usually admits 200 patients every day. One per cen...
Introduction
In a hospital that admits 200 patients daily, 1% typically require special room facilities. Hence, the average number of patients needing special rooms can be calculated as follows:
- Average patients needing special rooms = 1% of 200 = 2 patients.
Modeling the Situation
This scenario can be modeled using a Poisson distribution, where the average number of occurrences (λ) is equal to 2. The Poisson formula is used to find the probability of a number of events occurring in a fixed interval.
Probability of More Than 3 Patients
To calculate the probability of more than 3 patients requiring special room facilities, we need to find:
- P(X > 3) = 1 - P(X ≤ 3)
Where P(X ≤ 3) is the cumulative probability of 0, 1, 2, and 3 patients needing special rooms.
Calculating Cumulative Probability
Using the Poisson formula:
- P(X = k) = (λ^k * e^(-λ)) / k!
For k = 0, 1, 2, and 3:
- P(X = 0) = (2^0 * e^(-2)) / 0! = e^(-2)
- P(X = 1) = (2^1 * e^(-2)) / 1! = 2 * e^(-2)
- P(X = 2) = (2^2 * e^(-2)) / 2! = 2 * e^(-2)
- P(X = 3) = (2^3 * e^(-2)) / 3! = (8/6) * e^(-2)
Finally, sum these probabilities to find P(X ≤ 3) and then subtract from 1 to get P(X > 3).
Conclusion
By evaluating these probabilities, you can determine the likelihood of more than 3 patients requiring special room facilities on that particular morning. This insight is crucial for hospital management and allocation of resources.
In a hospital that admits 200 patients daily, 1% typically require special room facilities. Hence, the average number of patients needing special rooms can be calculated as follows:
- Average patients needing special rooms = 1% of 200 = 2 patients.
Modeling the Situation
This scenario can be modeled using a Poisson distribution, where the average number of occurrences (λ) is equal to 2. The Poisson formula is used to find the probability of a number of events occurring in a fixed interval.
Probability of More Than 3 Patients
To calculate the probability of more than 3 patients requiring special room facilities, we need to find:
- P(X > 3) = 1 - P(X ≤ 3)
Where P(X ≤ 3) is the cumulative probability of 0, 1, 2, and 3 patients needing special rooms.
Calculating Cumulative Probability
Using the Poisson formula:
- P(X = k) = (λ^k * e^(-λ)) / k!
For k = 0, 1, 2, and 3:
- P(X = 0) = (2^0 * e^(-2)) / 0! = e^(-2)
- P(X = 1) = (2^1 * e^(-2)) / 1! = 2 * e^(-2)
- P(X = 2) = (2^2 * e^(-2)) / 2! = 2 * e^(-2)
- P(X = 3) = (2^3 * e^(-2)) / 3! = (8/6) * e^(-2)
Finally, sum these probabilities to find P(X ≤ 3) and then subtract from 1 to get P(X > 3).
Conclusion
By evaluating these probabilities, you can determine the likelihood of more than 3 patients requiring special room facilities on that particular morning. This insight is crucial for hospital management and allocation of resources.
Community Answer
A renowned hospital usually admits 200 patients every day. One per cen...
NO, PLEASE SEND ME ANSWER THIS QUESTION SIR
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities??
Question Description
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities??.
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities??.
Solutions for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? defined & explained in the simplest way possible. Besides giving the explanation of
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities??, a detailed solution for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? has been provided alongside types of A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? theory, EduRev gives you an
ample number of questions to practice A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation 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.
|
© 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