Let X be a random variable following binomial distribution whose...

Let $n$ be the number of trials, $p$ be the probability of success, and $q$ be the probability of failure.

Given mean $= np = 200$

Given variance $= npq = 160$

Dividing variance by mean:

$\dfrac{npq}{np} = \dfrac{160}{200}$

$q = \dfrac{4}{5}$

Since $p + q = 1$, we have $p = 1 - \dfrac{4}{5} = \dfrac{1}{5}$

Substituting the value of $p$ in the mean equation:

$n \times \dfrac{1}{5} = 200$

$n = 1000$