a) In a certain country, the daily minimum temperature, in ${}^ \circ C$, in winter has the distribution $N\left( {8,{\text{ }}24} \right)$. Find the probability that a randomly chosen winter day in this country has a minimum temperature between $7{}^ \circ C$ and $12{}^ \circ C$.

The daily minimum temperature, in ${}^ \circ C$,  in another country in winter has a normal distribution with mean $\mu $ and standard deviation $2\mu $.

b) Find the proportion of winter days on which the minimum temperature is below zero.

c) 70 winter days are chosen at random. Find how many of these would be expected to have a minimum temperature which is more than three times the mean.

d) The probability of the minimum temperature being above $6{}^ \circ C$ on any winter day is 0.0735. Find the value of $\mu $.