A trucking firm delivers appliances for the large retail operation. The packages (or crates) have mean weight of 290 lb. And a variance of 2916. (Provide your answers correct to four decimal places.)
(a) If truck can carry 3880 lb. and 24 appliances need to be picked up, determine the probability that the 24 appliances will have an aggregate weight greater than the truck's capacity? Suppose that the 24 appliances represent the random sample.
(b) If the truck has a capacity of 7800 lb., determine the probability that it will be capable to carry the entire lot of 24 appliances?