Coffee Overflow

A coffee machine is regulated to charge 195 ml per cup with a standard deviation of 5 ml. Assuming the amount of fill is normally distributed, what is the probability that 200 ml cups will overflow?

For normal distributions,

P(X \ge 200) = P(z \ge \frac{200-\mu}{\sigma})  = P(z \ge \frac{200-195}{5})

Or you may use this simple R command

1 - pnorm(200, 195, 5)
0.1586553