Let X and Y be the life time (in hours) of two types of light bulbs, respectively. Assume \(X \sim \mathcal{N}(\mu_x, 689)\) and \(Y \sim \mathcal{N}(\mu_y, 735)\). Suppose a random sample of 23 type X light bulbs yields an average life time of 956.2 hours, and a random sample of 28 type Y light bulbs yields an average life time of 978.6 hours. Construct a 95\% confidence interval for \(\mu_x - \mu_y\).