1 It is known that the height \(H\), in metres, of trees of a certain kind has the distribution \(\mathrm { N } ( 12.5,10.24 )\). A scientist takes a random sample of 25 trees of this kind and finds the sample mean, \(\bar { H }\), of the heights.

1. State the distribution of \(\bar { H }\), giving the values of any parameters.
2. Find \(\mathrm { P } ( 12 < \bar { H } < 13 )\).