Garbage trucks entering a particular waste-management facility are weighed prior to offloading their contents. Let X = the total processing time for a randomly selected truck at this facility (waiting, weighing, and offloading). The article "Estimating Waste Transfer Station Delays Using GPS" (Waste Mgmt., 2008: 1742-1750) suggests the plausibility of a normal distribution with mean 13 min and standard deviation 4 min for X. Assume that this is in fact the correct distribution.

a. What is the probability that a single truck's processing time is between 12 and 15 min?

b. Consider a random sample of 16 trucks. What is the probability that the sample mean processing time is between 12 and 15 min?

c. Why is the probability in (b) much larger than the probability in (a)?

d. What is the probability that the sample mean processing time for a random sample of 16 trucks will be at least 20 min?