Question: The time between when an order is received on a factory floor and it is completed and ready to be moved to the warehouse is distributed according to following relationship:

f(x) = (1/36)[16x - 4x²] for 0 \(\le \) ?x \(\le \) ?3 .

a. Confirm that this is a probability function.

b. What is the average manufacturing time? The variance?

c. What is the probability that an order will take 2 days or less to