(a)[2]
Find the mean and variance of the daily revenue from chemical $A$.
(b)[6]
Find the probability that, on a day chosen at random, the revenue from chemical $A$ exceeds the revenue from chemical $B$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The daily masses, measured in kilograms, of chemicals $A$ and $B$ made by a factory are described by the independent random variables $X$ and $Y$ respectively, where $X \sim N(10.3,\,5.76)$ and $Y \sim N(11.4,\,9.61)$. The revenue from the chemicals is $\$2.50$ for each kilogram of $A$ and $\$3.25$ for each kilogram of $B$.