Probability of cup overflowing with double normal distribution

[badatmath123]

A coffee machine fills a cup automatically with a volume of coffee that is normally distributed with a mean of 2.2 dl and a standard deviation of 0.15 dl. The cups used can hold a volume of coffee with a mean of 2.4 dl and a standard deviation of 0.3 dl. The volume of coffee dispensed by the machine and the volume of a cup are independent. What is the probability that it will overflow during a random filling of a cup?

My problem is the two normal distribution variables, i only know how to handle one. Could anyone please help me with this?

 

[BigBeachBanana]

Define the volume the coffee machine fills as [imath]X\sim(2.2,0.15)[/imath] and the volume the coffee cup can hold as
[imath]Y\sim(2.4,0.3)[/imath]. You're seeking [imath]\Pr(X-Y >0)[/imath]. What is the mean of and standard deviation of [imath]Z=X-Y[/imath]?

 

[blamocur]

What is the mean of and standard deviation of Z=X−Y?

Also, what is the distribution of X-Y?