Each drink from a coffee machine contains $X{\text{ }}c{m^3}$ of coffee and $Y{\text{ }}c{m^3}$ of milk, where $X$ and $Y$ are independent variables with $X \sim N\left( {184,{\text{ }}{{15}^2}} \right)$ and $Y \sim N\left( {50,{\text{ }}{8^2}} \right)$. If the total volume of the drink is less than $200{\text{ }}c{m^3}$ the customer receives the drink without charge.
a) Find the percentage of drinks which customers receive without charge.
b) Find the probability that, in a randomly chosen drink, the volume of coffee is more than 4 times the volume of milk.
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