1. Maintaining a constant temperature in a pipe wall in some hot process applications is critical. A new technique utilizes certain BT elements to maintain and stabilize the temperature. Without these elements, the pipe wall temperature uniformly ranges from 260 to 290F. When several BT elements are attached to the pipes, the wall temperature varies uniformly from 278 to 285F.

a. Ideally, the pipe wall temperature should range between 280 and 284F. What is the probability that the temperature will fall into this ideal range when no BT elements are used? And when BT elements are used?

b. When the temperature is 268F or lower, the hot liquid plastic hardens (or "plates"), causing a buildup in the piping. What is the probability of the plastic plating when no BT elements are used? And when BT elements are attached?

2. Between 10pm and 11pm on Friday night, The Best Crust Pizza gets an average of 4.0 online orders per hour.

a. Find the average waiting time until the next online order.

b. What is the probability that the orders are less than average waiting apart?

c. What is the probability that the orders are more than 30 minutes apart?

d. What is the upper 25 percent of waiting time until the next online order? (Hint: determine t such that p(x>t)=0.25)