A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 300 lb. and a variance of 2209. (Give your answers correct to four decimal places.)
(a) If a truck can carry 4130 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 7940 lb., what is the probability that it will be able to carry the entire lot of 25 appliances?