If the mean of a binomial distribution is 5 and its standard deviation is 2, then the number of trials is:

25

The correct answer is Option (3) → 25

$\text{Mean} = np = 5$

$\text{Standard deviation} = \sqrt{npq} = 2$

$npq = 4$

$np = 5 \;\Rightarrow\; q = \frac{4}{5}$

$p = 1 - q = 1 - \frac{4}{5} = \frac{1}{5}$

$np = 5 \;\Rightarrow\; n \cdot \frac{1}{5} = 5$

$n = 25$

The number of trials is 25.