(i)[2]
Calculate the probability that a fir tree chosen at random from this forest has a height below $45$ metres.
(ii)[2]
Calculate the probability that a fir tree chosen at random from this forest has a height within $5$ metres of the mean.
(iii)[5]
In a different forest, the heights of another kind of fir tree are represented by a normal distribution. A scientist records the heights of $500$ randomly selected trees of this type. He discovers that $48$ trees are shorter than $10\,\text{m}$ and $76$ trees are taller than $24\,\text{m}$. Find the mean and standard deviation of the heights of trees of this type.