2 The lengths of time people take to complete a certain type of puzzle are normally distributed with mean 48.8 minutes and standard deviation 15.6 minutes. The random variable \(X\) represents the time taken in minutes by a randomly chosen person to solve this type of puzzle. The times taken by random samples of 5 people are noted. The mean time \(\bar { X }\) is calculated for each sample.

1. State the distribution of \(\bar { X }\), giving the values of any parameters.
2. Find \(\mathrm { P } ( \bar { X } < 50 )\).