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(11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None?
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(11) Suppose that weather records show that on an average 5 out of 31 ...
Solution:
Given,
p = probability of rainy day = 5/31
q = probability of non-rainy day = 1 - p = 26/31
We need to find the probability that at most 3 days will be rainy in October.
Let X be the number of rainy days in October.
Then,
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Using the binomial distribution formula, we have:
P(X = r) = nCr * p^r * q^(n-r)
where n = 31 (total number of days in October)
P(X = 0) = 31C0 * (5/31)^0 * (26/31)^31 = 0.0336
P(X = 1) = 31C1 * (5/31)^1 * (26/31)^30 = 0.1547
P(X = 2) = 31C2 * (5/31)^2 * (26/31)^29 = 0.2857
P(X = 3) = 31C3 * (5/31)^3 * (26/31)^28 = 0.2802
Therefore,
P(X ≤ 3) = 0.0336 + 0.1547 + 0.2857 + 0.2802 = 0.7542
Hence, the probability that the next October will have at most three rainy days is 0.7542 or 75.42%.
Therefore, the correct option is (d) None.
Note: The options given in the question are not correct.
Given,
p = probability of rainy day = 5/31
q = probability of non-rainy day = 1 - p = 26/31
We need to find the probability that at most 3 days will be rainy in October.
Let X be the number of rainy days in October.
Then,
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Using the binomial distribution formula, we have:
P(X = r) = nCr * p^r * q^(n-r)
where n = 31 (total number of days in October)
P(X = 0) = 31C0 * (5/31)^0 * (26/31)^31 = 0.0336
P(X = 1) = 31C1 * (5/31)^1 * (26/31)^30 = 0.1547
P(X = 2) = 31C2 * (5/31)^2 * (26/31)^29 = 0.2857
P(X = 3) = 31C3 * (5/31)^3 * (26/31)^28 = 0.2802
Therefore,
P(X ≤ 3) = 0.0336 + 0.1547 + 0.2857 + 0.2802 = 0.7542
Hence, the probability that the next October will have at most three rainy days is 0.7542 or 75.42%.
Therefore, the correct option is (d) None.
Note: The options given in the question are not correct.
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(11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None?
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(11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None? 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 (11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None?.
(11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None? 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 (11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (11) Suppose that weather records 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 the probability that the next October will have at most three rainy days is: a. 0.4403 b. 0.2403 c. 0.3403 d. None?.
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