A drink dispenser pours lemonade into a cup when a coin is inserted into the machine. The amount of lemonade delivered is normally distributed with mean 260 ml and standard deviation 10 ml. The capacity of the cup is 275 ml.

a) Find the probability that the cup overflows.

b) On an occasion, 5 such cups of lemonade were purchased at random. Find the probability that not more than 1 cup contains less than 250 ml.

c) The standard deviation of the amount of lemonade per cup is fixed, but the mean can be altered. Find the suitable value of the mean so that not more than 5% of the cups will contain less than 250 ml of lemonade.