Let the random variable \(X\) represent the number of plants producing pink flowers in a box of 100. \(X\) follows a binomial distribution with parameters \(n = 100\) and \(p = 0.3\).

To approximate this binomial distribution, we use a normal distribution with mean \(\mu\) and variance \(\sigma^2\).

Calculate the mean: \(\mu = np = 100 \times 0.3 = 30\).

Calculate the variance: \(\sigma^2 = np(1-p) = 100 \times 0.3 \times 0.7 = 21\).

Thus, \(X \sim N(30, 21)\).

We need to find \(P(X < 35)\). Using a continuity correction, this becomes \(P(X < 34.5)\).

Standardize the variable: \(Z = \frac{34.5 - 30}{\sqrt{21}} = \frac{4.5}{\sqrt{21}} \approx 0.9820\).

Using the standard normal distribution table, \(\Phi(0.9820) \approx 0.837\).

Therefore, the probability that a box contains fewer than 35 plants which produce pink flowers is \(0.837\).