6 The lengths, in cm, of trout in a fish farm are normally distributed. 96\% of the lengths are less than 34.1 cm and 70\% of the lengths are more than 26.7 cm .
- Find the mean and the standard deviation of the lengths of the trout.
In another fish farm, the lengths of salmon, \(X \mathrm {~cm}\), are normally distributed with mean 32.9 cm and standard deviation 2.4 cm .
- Find the probability that a randomly chosen salmon is 34 cm long, correct to the nearest centimetre.
- Find the value of \(t\) such that \(\mathrm { P } ( 31.8 < X < t ) = 0.5\).