4. Consider a random sample \( \{x_1, \dots, x_n\} \) from the distribution with mean \( \mu \) and known variance \( \sigma^2 \). Define \( \bar{x} = n^{-1} \sum_{i=1}^{i=n} x_i \), \( s_1^2 = (n-2)^{-1} \sum_{i=1}^{i=n} (x_i - \mu)^2 \), and \( s_2^2 = (n-2)^{-1} \sum_{i=1}^{i=n} (x_i - \bar{x})^2 \). If n=60, the distributions of \( (n-2)s_1^2/\sigma^2 \) and \( (n-2)s_2^2/\sigma^2 \) are ________ and ________, respectively. (10%) (Justify your answers)