Given that the distribution is normal with mean \\(\mu = 15.8 \\\) and standard deviation \\(\sigma = 4.2 \\\), we need to find the value of \\(k \\\) such that \\(P(X < k) = 0.75 \\\).

First, find the z-score corresponding to the cumulative probability of 0.75. From standard normal distribution tables, \\(z = 0.674 \\\).

Use the z-score formula:

\\(z = \frac{k - \mu}{\sigma} \\\)

Substitute the known values:

\\(0.674 = \frac{k - 15.8}{4.2} \\\)

Solve for \\(k \\\):

\\(k - 15.8 = 0.674 \times 4.2 \\\)

\\(k - 15.8 = 2.8308 \\\)

\\(k = 15.8 + 2.8308 \\\)

\\(k = 18.6308 \\\)

Rounding to one decimal place, \\(k = 18.6 \\\).