Let the random variable \(X\) represent the number of people who enjoy watching Historical Drama. \(X\) follows a binomial distribution with parameters \(n = 160\) and \(p = 0.1\).

We approximate this binomial distribution with a normal distribution. First, calculate the mean \(np\) and variance \(npq\):

\(np = 160 \times 0.1 = 16\)

\(npq = 160 \times 0.1 \times 0.9 = 14.4\)

Using the normal approximation, we have \(X \sim N(16, 14.4)\).

We need to find \(P(X > 17)\). Using continuity correction, this is \(P(X \geq 17.5)\).

Standardize the variable:

\(P(X \geq 17.5) = P\left( Z \geq \frac{17.5 - 16}{\sqrt{14.4}} \right) = P(Z \geq 0.3953)\)

Using standard normal distribution tables, \(P(Z \geq 0.3953) = 1 - P(Z < 0.3953) = 1 - 0.6536 = 0.346\).