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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?
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A renowned hospital usually admits 200 patients every day. One per cen...
Solution:
Given:
- The hospital admits 200 patients every day.
- On average, 1% of the patients require special room facilities.
- Only one special room is available on a particular morning.
To find:
- The probability that more than 3 patients would require special room facilities.
Approach:
We can use the Poisson distribution to solve this problem because it is a discrete probability distribution that deals with the number of events occurring in a given time or space.
Formula for Poisson Distribution:
P(x) = (e^(-λ) * λ^x) / x!
where,
- P(x) is the probability of x events occurring in a certain time or space interval.
- e is the base of the natural logarithm.
- λ (lambda) is the mean or average number of events occurring in the interval.
- x is the number of events occurring in the interval.
Steps:
1. Find the average number of patients requiring special room facilities using the given information.
- 1% of 200 patients = 2 patients
- Therefore, λ = 2
2. Find the probability that exactly 0, 1, 2, and 3 patients require special room facilities using the Poisson distribution formula.
- P(0) = (e^(-2) * 2^0) / 0! = 0.135
- P(1) = (e^(-2) * 2^1) / 1! = 0.271
- P(2) = (e^(-2) * 2^2) / 2! = 0.271
- P(3) = (e^(-2) * 2^3) / 3! = 0.180
3. Find the probability that more than 3 patients require special room facilities by subtracting the sum of probabilities from 0 to 3 from 1.
- P(x > 3) = 1 - (P(0) + P(1) + P(2) + P(3))
- P(x > 3) = 1 - (0.135 + 0.271 + 0.271 + 0.180)
- P(x > 3) = 0.143
Therefore, the probability that more than 3 patients would require special room facilities is 0.143 or 14.3%.
Answer: The probability that more than 3 patients would require special room facilities is 0.143 or 14.3%.
Given:
- The hospital admits 200 patients every day.
- On average, 1% of the patients require special room facilities.
- Only one special room is available on a particular morning.
To find:
- The probability that more than 3 patients would require special room facilities.
Approach:
We can use the Poisson distribution to solve this problem because it is a discrete probability distribution that deals with the number of events occurring in a given time or space.
Formula for Poisson Distribution:
P(x) = (e^(-λ) * λ^x) / x!
where,
- P(x) is the probability of x events occurring in a certain time or space interval.
- e is the base of the natural logarithm.
- λ (lambda) is the mean or average number of events occurring in the interval.
- x is the number of events occurring in the interval.
Steps:
1. Find the average number of patients requiring special room facilities using the given information.
- 1% of 200 patients = 2 patients
- Therefore, λ = 2
2. Find the probability that exactly 0, 1, 2, and 3 patients require special room facilities using the Poisson distribution formula.
- P(0) = (e^(-2) * 2^0) / 0! = 0.135
- P(1) = (e^(-2) * 2^1) / 1! = 0.271
- P(2) = (e^(-2) * 2^2) / 2! = 0.271
- P(3) = (e^(-2) * 2^3) / 3! = 0.180
3. Find the probability that more than 3 patients require special room facilities by subtracting the sum of probabilities from 0 to 3 from 1.
- P(x > 3) = 1 - (P(0) + P(1) + P(2) + P(3))
- P(x > 3) = 1 - (0.135 + 0.271 + 0.271 + 0.180)
- P(x > 3) = 0.143
Therefore, the probability that more than 3 patients would require special room facilities is 0.143 or 14.3%.
Answer: The probability that more than 3 patients would require special room facilities is 0.143 or 14.3%.
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A renowned hospital usually admits 200 patients every day. One per cen...
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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?
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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?.
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