(i)[5]
Determine the proportion of gem stones that lie in each of these three categories.
(ii)[4]
Determine the value of $k$ so that $P(k < X < 2.5) = 0.8$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Gem stones drawn from one mine have weights, $X$ grams, and these are normally distributed with mean $1.9\text{ g}$ and standard deviation $0.55\text{ g}$. For sale, the gem stones are split into three weight bands: Small: below $1.2\text{ g}$; Medium: from $1.2\text{ g}$ to $2.5\text{ g}$; Large: above $2.5\text{ g}$.