If mean and standard deviation of a binomial distribution is 10 and 2respectively; q will be ___(a) 1(b) 0.8(c) 0.6(d) 0.4
Question
If mean and standard deviation of a binomial distribution is 10 and 2 respectively; q will be ___
(a) 1
(b) 0.8
(c) 0.6
(d) 0.4
Solution
In a binomial distribution, the mean (μ) and standard deviation (σ) are given by the formulas:
μ = np σ = sqrt(npq)
where: n = number of trials p = probability of success q = probability of failure (1-p)
Given that μ = 10 and σ = 2, we can use these formulas to find the value of q.
First, we can square the formula for the standard deviation to get rid of the square root:
σ^2 = npq
Substituting the given values:
4 = 10q
Solving for q gives:
q = 4/10 = 0.4
So, the answer is (d) 0.4.
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