2. The continuous random variable \(X\) represents the error, in mm, made when a machine cuts piping to a target length. The distribution of \(X\) is rectangular over the interval \([ - 5.0,5.0 ]\). Find

1. \(\mathrm { P } ( X < - 4.2 )\),
2. \(\mathrm { P } ( | X | < 1.5 )\). A supervisor checks a random sample of 10 lengths of piping cut by the machine.
3. Find the probability that more than half of them are within 1.5 cm of the target length.
   (3 marks)
   If \(X < - 4.2\), the length of piping cannot be used. At the end of each day the supervisor checks a random sample of 60 lengths of piping.
4. Use a suitable approximation to estimate the probability that no more than 2 of these lengths of piping cannot be used.
   (5 marks)