Step 1 :The problem is asking for the distribution of the sample mean, denoted as \(x^{-}\).
Step 2 :We know that the distribution of the sample mean follows a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. This is a result of the Central Limit Theorem.
Step 3 :The given population mean (mu) is 12 months and the population standard deviation (sigma) is 1.3 months. The sample size (n) is 17.
Step 4 :The mean of the sample mean distribution (mu_x_bar) is the same as the population mean, which is 12 months.
Step 5 :The standard deviation of the sample mean distribution (sigma_x_bar) is the population standard deviation divided by the square root of the sample size, which is approximately 0.3153 months.
Step 6 :Final Answer: The distribution of the sample mean \(x^{-}\) is normally distributed with mean \(\boxed{12}\) months and standard deviation \(\boxed{0.3153}\) months.