(a)[3]
It is given that $X \sim N(31.4, 3.6)$. Find the probability that a randomly selected value of $X$ lies below $29.4$.
(b)[5]
The lengths of fish of a particular species are modelled by a normal distribution. A scientist measures the lengths of 400 randomly selected fish of this species. He records that 42 fish are shorter than $12\text{ cm}$ and 58 fish are longer than $19\text{ cm}$. Find estimates for the mean and standard deviation of the lengths of fish of this species.