A coffee machine is adjusted to provide a population mean of 110ml of coffee per cup and a standard deviation of 5 ml. The volume of coffee per cup is assumed to have a normal distribution. The machine is checked periodically by sampling 12 cups of coffee. If the mean volume, Y, of those 12 cups in ml falls in the interval (110- 2 cy~) < y < (110 + 2 o~ ), no adjustment is made. Otherwise, the machine is adjusted.

a) If a 12-cup test gives a mean volume of 107.0 ml, what should be done?

b) What fraction of the total number of 12-cup tests would lead to an adjust-

ment being made, even if the machine had not changed from its original

correct setting?

c) How many cups should be sampled randomly so there is 99% confidence

that the mean volume of the sample will lie within +2 ml of 110ml when the machine is correctly adjusted?