5 When a particular make of tennis ball is dropped from a vertical distance of 250 cm on to concrete, the height, \(X\) centimetres, to which it first bounces may be assumed to be normally distributed with a mean of 140 and a standard deviation of 2.5.

1. Determine:
   1. \(\mathrm { P } ( X < 145 )\);
   2. \(\mathrm { P } ( 138 < X < 142 )\).
2. Determine, to one decimal place, the maximum height exceeded by \(85 \%\) of first bounces.
3. Determine the probability that, for a random sample of 4 first bounces, the mean height is greater than 139 cm .