1. A coffee-vending machine is set to dispense amounts of coffee per cup that follows a normal distribution with a mean of 200 mL and a standard deviation of 10 mL. Let the random variable X be amount of coffee (in mL) per cup.
a. What is the probability that a randomly selected cup will contain more than 225 mL of coffee as dispensed by the machine?
b. What proportion of the cups will contain anywhere between 198 and 215 mL of coffee?