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Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days?
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Suppose that weather record show that on an average 5 out of 31 days i...
Problem Statement: Suppose that weather records show that on average 5 out of 31 days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial, find the probability that the next October will have at most 3 rainy days.
Solution:
Step 1: Identify the parameters of the problem
- The number of trials (n) = 31 (since there are 31 days in October)
- The probability of success (p) = 5/31 (since on average, 5 out of 31 days are rainy)
- The number of successes we want (x) = 0, 1, 2, or 3 (since we want to find the probability of at most 3 rainy days)
Step 2: Calculate the probabilities
Using the binomial probability formula, we can calculate the probability of getting at most 3 rainy days:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (31C0)(5/31)^0(26/31)^31 + (31C1)(5/31)^1(26/31)^30 + (31C2)(5/31)^2(26/31)^29 + (31C3)(5/31)^3(26/31)^28
= 0.097 + 0.213 + 0.268 + 0.211
= 0.789
Therefore, the probability that the next October will have at most 3 rainy days is 0.789 or 78.9%.
Conclusion: The probability that the next October will have at most 3 rainy days is 0.789 or 78.9%.
Solution:
Step 1: Identify the parameters of the problem
- The number of trials (n) = 31 (since there are 31 days in October)
- The probability of success (p) = 5/31 (since on average, 5 out of 31 days are rainy)
- The number of successes we want (x) = 0, 1, 2, or 3 (since we want to find the probability of at most 3 rainy days)
Step 2: Calculate the probabilities
Using the binomial probability formula, we can calculate the probability of getting at most 3 rainy days:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (31C0)(5/31)^0(26/31)^31 + (31C1)(5/31)^1(26/31)^30 + (31C2)(5/31)^2(26/31)^29 + (31C3)(5/31)^3(26/31)^28
= 0.097 + 0.213 + 0.268 + 0.211
= 0.789
Therefore, the probability that the next October will have at most 3 rainy days is 0.789 or 78.9%.
Conclusion: The probability that the next October will have at most 3 rainy days is 0.789 or 78.9%.
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Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days?
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Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days? 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 Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days?.
Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days? 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 Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that weather record show that on an average 5 out of 31 days in October are rainy days assuming a binomial distribution with each day of October as an independent trial then probability that the next October will have at most 3 rainy days?.
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