2 The diameter, \(D\) millimetres, of an American pool ball may be modelled by a normal random variable with mean 57.15 and standard deviation 0.04 .
- Determine:
- \(\mathrm { P } ( D < 57.2 )\);
- \(\mathrm { P } ( 57.1 < D < 57.2 )\).
- A box contains 16 of these pool balls. Given that the balls may be regarded as a random sample, determine the probability that:
- all 16 balls have diameters less than 57.2 mm ;
- the mean diameter of the 16 balls is greater than 57.16 mm .