A grocery store sells X hundred kilograms of rice every day, where the distribution of the random variable X is of the following form:
Suppose that this grocery store's total sales of rice do not reach 600 kilo-grams on any given day.
(a) Find the value of k.
(b) What is the probability that the store sells between 200 and 400 kilograms of rice next Thursday?
(c) What is the probability that the store sells over 300 kilograms of rice next Thursday?
(d) We are given that the store sold at least 300 kilograms of rice last Friday. What is the probability that it did not sell more than 400 kilograms on that day?