Let \(p = 0.25\) and \(n = 160\). The mean of the distribution is \(n \times p = 160 \times 0.25 = 40\).

The variance is \(n \times p \times (1-p) = 160 \times 0.25 \times 0.75 = 30\).

We approximate the binomial distribution with a normal distribution: \(X \sim N(40, 30)\).

To find \(P(X < 50)\), we use the continuity correction: \(P(X < 49.5)\).

Standardize: \(Z = \frac{49.5 - 40}{\sqrt{30}} \approx 1.734\).

Thus, \(P(Z < 1.734) = 0.959\).