Suppose that instant coffee comes in two sizes, 10-ounce jars and 30-ounce jars.
Let $X$ be the actual weight of coffee in a 10-ounce jar and assume that $X$ has a normal distribution with a mean 10.1 ounces and standard deviation 0.2 ounces.
Let $Y$ be the actual weight of coffee in a 30-ounce jar and assume that $Y$ has a normal distribution with mean 30.4 ounces and standard deviation 0.42 ounces.
Assume that the weights $X$ and $Y$ are independent random variables.
Find the probability that total weight of coffee is three 10-ounce jars in greater than the weight in one 30-ounce jar.