find the binomial distribution for which the mean and variance are 12 and 3 respectively .

Explanation

To find the binomial distribution for which the mean is 12 and the variance is 3, we can follow these steps:

### Step 1: Understand the relationships for mean and variance in a binomial distribution
In a binomial distribution, the mean (μ) and variance (σ²) are given by:
- Mean: \( \mu = n \cdot p \)
- Variance: \( \sigma^2 = n \cdot p \cdot q \)
where \( n \) is the number of trials, \( p \) is the probability of success, and \( q = 1 - p \) is the probability of failure.

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