You are throwing a party and ll a bowl with 63 ounces of punch. Suppose the expected size of each cup of punch is 2 ounces and the standard deviation of the size of a cup is 1/2 ounce and each cup is poured independently.
(a) Suppose each cup's size is independently drawn from the distribu- tion. What is the approximate probability that 36 cups will have been poured before the bowl is empty? (Hint: you can look up the standard normal cdf, (c), for any value c in Stata by typing display normal([enter c here])").
(b) Suppose that all the cups' sizes are identical, but that their precise size is unknown - only that it is drawn from the given distribution. What is the approximate probability that 36 cups will have been poured before the bowl is empty?
It part b, normal distribution is asummed at a given moment.