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In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is
- a)6
- b)8
- c)12
- d)10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a Binomial distribution, the probability of getting a success is 1/...
Binomial Distribution
Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of trials with a given probability of success in each trial. It is denoted by B(n,p), where n is the number of trials and p is the probability of success.
Formula for Mean and Standard Deviation
The mean or expected value of a binomial distribution is given by:
μ = np
The standard deviation of a binomial distribution is given by:
σ = √(np(1-p))
Given Information
In this question, the probability of getting a success is 1/4 and the standard deviation is 3.
Calculation
We can use the formula for standard deviation to find the value of p:
σ = √(np(1-p)) = 3
Squaring both sides, we get:
np(1-p) = 9
Multiplying both sides by 4, we get:
4np(1-p) = 36
Expanding, we get:
4np - 4np^2 = 36
4np^2 - 4np + 36 = 0
Dividing both sides by 4, we get:
np^2 - np + 9 = 0
Using the quadratic formula, we get:
p = (1 ± √37i)/2n
Since p is a probability, it must be between 0 and 1. Therefore, we take the negative root:
p = (1 - √37i)/2n
Substituting the value of p in the formula for mean, we get:
μ = np = n(1 - √37i)/2n = (1 - √37i)/2
Simplifying, we get:
μ = 0.5 - 0.5√37i
Therefore, the mean is approximately 0.5.
Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of trials with a given probability of success in each trial. It is denoted by B(n,p), where n is the number of trials and p is the probability of success.
Formula for Mean and Standard Deviation
The mean or expected value of a binomial distribution is given by:
μ = np
The standard deviation of a binomial distribution is given by:
σ = √(np(1-p))
Given Information
In this question, the probability of getting a success is 1/4 and the standard deviation is 3.
Calculation
We can use the formula for standard deviation to find the value of p:
σ = √(np(1-p)) = 3
Squaring both sides, we get:
np(1-p) = 9
Multiplying both sides by 4, we get:
4np(1-p) = 36
Expanding, we get:
4np - 4np^2 = 36
4np^2 - 4np + 36 = 0
Dividing both sides by 4, we get:
np^2 - np + 9 = 0
Using the quadratic formula, we get:
p = (1 ± √37i)/2n
Since p is a probability, it must be between 0 and 1. Therefore, we take the negative root:
p = (1 - √37i)/2n
Substituting the value of p in the formula for mean, we get:
μ = np = n(1 - √37i)/2n = (1 - √37i)/2
Simplifying, we get:
μ = 0.5 - 0.5√37i
Therefore, the mean is approximately 0.5.
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In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean isa)6b)8c)12d)10Correct answer is option 'C'. Can you explain this answer?
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In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean isa)6b)8c)12d)10Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean isa)6b)8c)12d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean isa)6b)8c)12d)10Correct answer is option 'C'. Can you explain this answer?.
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