A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 294 lb. and a variance of 2401. (Give your answers correct to four decimal places.)
(a) If a truck can carry 3850 lb. and 29 appliances need to be picked up, what is the probability that the 29 appliances will have an aggregate weight greater than the truck's capacity? Assume that the 29 appliances represent a random sample.
(b) If the truck has a capacity of 7990 lb., what is the probability that it will be able to carry the entire lot of 29 appliances?