A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 291 lb. and a variance of 2809. (Give your answers correct to four decimal places.)
(a) If a truck can carry 4000 lb. and 26 appliances need to be picked up, what is the probability that the 26 appliances will have an aggregate weight greater than the truck's capacity? Assume that the 26 appliances represent a random sample.
(b) If the truck has a capacity of 8030 lb., what is the probability that it will be able to carry the entire lot of 26 appliances?