We are given that 90% of the weights lie between (830 - w) kg and (830 + w) kg. This implies that 5% of the weights are below (830 - w) kg and 5% are above (830 + w) kg.

Thus, the probability that a giraffe weighs less than (830 + w) kg is 95%, which corresponds to a z-score of 1.645 for a standard normal distribution.

Using the standardization formula:

\(\frac{(830 + w) - 830}{120} = \frac{w}{120} = 1.645\)

Solving for \(w\):

\(w = 1.645 \times 120 = 197.4\)

Since \(w\) must be an integer, we round to \(w = 197\).