Suppose that the number of coffees that the university cafeteria sells per day during the trimester is normally distributed with a mean of 223 cups, and a standard deviation of 39 cups. Calculate the following values.

(a) Find the probability that the amount of coffee sold (in cups per day) is greater than 289.

(b) Find the probability that the amount of coffee sold (in cups per day) is less than 289.

(c) Find the probability that the amount of coffee sold (in cups per day) is greater than 147 and less than 277.

Binomial Probabilities Table X P(X) P(X) P(>=X) 0 0.0026 0.0026 0.0000 0.9974 1.0000 1 0.0262 0.0288 0.0026 0.9712 0.9974 2 0.1116 0.1404 0.0288 0.8596 0.9712 3 0.2533 0.3937 0.1404 0.6063 0.8596 4 0.3235 0.7172 0.3937 0.2828 0.6063 5 0.2203 0.9375 0.7172 0.0625 0.2828 6 0.0625 1.0000 0.9375 0.0000 0.0625