The sum of mean and variance of a binomial distribution is 15 and the sum of their squares is 117. Determine the distribution.

Explanation

To solve the problem step by step, we will use the properties of the binomial distribution, particularly the mean and variance.

### Step 1: Define Mean and Variance
For a binomial distribution with parameters \( n \) (number of trials) and \( p \) (probability of success), the mean \( \mu \) and variance \( \sigma^2 \) are given by:
- Mean: \( \mu = np \)
- Variance: \( \sigma^2 = npq \), where \( q = 1 - p \)

### Step 2: Set Up the Equations
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