A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 305 lb. and a variance of 2916. (Give your answers correct to four decimal places.)
(a) If a truck can carry 3990 lb. and 25 appliances need to be picked up, what is the probability that the 25 appliances will have an aggregate weight greater than the truck's capacity? Assume that the 25 appliances represent a random sample.
(b) If the truck has a capacity of 7890 lb., what is the probability that it will be able to carry the entire lot of 25 appliances?