1 It is known that the number, \(N\), of words contained in the leading article each day in a certain newspaper can be modelled by a normal distribution with mean 352 and variance 29. A researcher takes a random sample of 10 leading articles and finds the sample mean, \(\bar { N }\), of \(N\).

1. State the distribution of \(\bar { N }\), giving the values of any parameters.
2. Find \(\mathrm { P } ( \bar { N } > 354 )\).