2. (i) The continuous random variable \(X\) is uniformly distributed over the interval \([ a , b ]\) Given that \(\mathrm { P } ( 8 < X < 14 ) = \frac { 1 } { 5 }\) and \(\mathrm { E } ( X ) = 11\)

1. write down \(\mathrm { P } ( X > 14 )\)
2. find \(\mathrm { P } ( 6 X > a + b )\)
   (ii) Susie makes a strip of pasta 45 cm long. She then cuts the strip of pasta, at a randomly chosen point, into two pieces. The random variable \(S\) is the length of the shortest piece of pasta.
3. Write down the distribution of \(S\)
4. Calculate the probability that the shortest piece of pasta is less than 12 cm long. Susie makes 20 strips of pasta, all 45 cm long, and separately cuts each strip of pasta, at a randomly chosen point, into two pieces.
5. Calculate the probability that exactly 6 of the pieces of pasta are less than 12 cm long.