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What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively
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What is the number of trials of a binomial distribution having mean an...
Calculating the Number of Trials in a Binomial Distribution
Assuming the mean and standard deviation of a binomial distribution as 3 and 1.5 respectively, we can calculate the number of trials in the following manner:
Step 1: Identify the formula for mean and standard deviation of a binomial distribution
The mean and standard deviation of a binomial distribution can be calculated using the following formulas:
- Mean = n * p
- Standard deviation = sqrt(n * p * q)
where n is the number of trials, p is the probability of success, and q is the probability of failure.
Step 2: Substitute the given values of mean and standard deviation
Substituting the given values of mean and standard deviation in the above formulas, we get:
- 3 = n * p
- 1.5 = sqrt(n * p * q)
Step 3: Solve for p and q
From the first equation, we can solve for p as:
- p = 3 / n
Substituting this value of p in the second equation, we get:
- 1.5 = sqrt(n * (3 / n) * q)
- 1.5 = sqrt(3q)
- 2.25 = 3q
- q = 0.75
Step 4: Substitute the values of p and q in the first equation
Substituting the values of p and q in the first equation, we get:
- 3 = n * (3 / n)
- n = 3 / (3 / n)
- n = 9
Step 5: Interpretation
Therefore, the number of trials in the binomial distribution is 9. This means that the experiment was repeated 9 times to obtain the given mean and standard deviation.
Community Answer
What is the number of trials of a binomial distribution having mean an...
Ans: n=12;. np=3, root of npq=1.5, q=0.75, p=0.25, p=1-q. then n=12
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What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively
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What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively 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 What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively.
What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively 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 What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively.
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