A scientist found that the time taken, \(M\) minutes, to carry out an experiment can be modelled by a normal random variable with mean 155 minutes and standard deviation 3.5 minutes.
Find
\(\mathrm { P } ( M > 160 )\).
\(\mathrm { P } ( 150 \leqslant M \leqslant 157 )\).
the value of \(m\), to 1 decimal place, such that \(\mathrm { P } ( M \leqslant m ) = 0.30\).