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Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days?
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Suppose that weather records show that on an average 5 out of 3q days ...
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Suppose that weather records show that on an average 5 out of 3q days ...
Solution:
Defining the problem
We have to find the probability of having at most three rainy days in the next October. We know that on average, 5 out of 3q days in October are rainy days.
Identifying the distribution
We assume a binomial distribution with each day of October as an independent trial. The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of trials.
Finding the parameters
The parameters of the binomial distribution are n and p, where n is the number of trials and p is the probability of success. In our case, n is the number of days in October, which is 31, and p is the probability of having a rainy day, which is 5/31.
Calculating the probability
To find the probability of having at most three rainy days in October, we need to calculate the cumulative probability of having 0, 1, 2, or 3 rainy days. We can use a binomial probability table or a binomial calculator to find these probabilities.
Using a binomial probability table, we get:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X ≤ 3) = 0.378
Therefore, the probability of having at most three rainy days in the next October is 0.378 or 37.8%.
Conclusion
In conclusion, assuming a binomial distribution with each day of October as an independent trial, the probability of having at most three rainy days in the next October is 0.378 or 37.8%.
Defining the problem
We have to find the probability of having at most three rainy days in the next October. We know that on average, 5 out of 3q days in October are rainy days.
Identifying the distribution
We assume a binomial distribution with each day of October as an independent trial. The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of trials.
Finding the parameters
The parameters of the binomial distribution are n and p, where n is the number of trials and p is the probability of success. In our case, n is the number of days in October, which is 31, and p is the probability of having a rainy day, which is 5/31.
Calculating the probability
To find the probability of having at most three rainy days in October, we need to calculate the cumulative probability of having 0, 1, 2, or 3 rainy days. We can use a binomial probability table or a binomial calculator to find these probabilities.
Using a binomial probability table, we get:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X ≤ 3) = 0.378
Therefore, the probability of having at most three rainy days in the next October is 0.378 or 37.8%.
Conclusion
In conclusion, assuming a binomial distribution with each day of October as an independent trial, the probability of having at most three rainy days in the next October is 0.378 or 37.8%.
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Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days?
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Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days?.
Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that weather records show that on an average 5 out of 3q days in October are rainy days. Assuming a binomial distribution with each day of October as an independent trial,th the probability that the next October will have at most three rainy days?.
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