A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 298 lb. and a variance of 2704. (Give your answers correct to four decimal places.)
(a) If a truck can carry 4120 lb. and 24 appliances need to be picked up, what is the probability that the 24 appliances will have an aggregate weight greater than the truck's capacity? Assume that the 24 appliances represent a random sample.
(b) If the truck has a capacity of 7960 lb., what is the probability that it will be able to carry the entire lot of 24 appliances?