A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 303 lb. and a variance of 2809. (Give your answers correct to four decimal places.)
(a) If a truck can carry 4110 lb. and 21 appliances need to be picked up, what is the probability that the 21 appliances will have an aggregate weight greater than the truck's capacity? Assume that the 21 appliances represent a random sample.
(b) If the truck has a capacity of 8140 lb., what is the probability that it will be able to carry the entire lot of 21 appliances?