A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 306 lb. and a variance of 2209. (Give your answers correct to four decimal places.)

Question

(a) If a truck can carry 3940 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 7810 lb., what is the probability that it will be able to carry the entire lot of 25 appliances?

Answer 1

Hello. I managed to solve (a)

Expected aggregate weight = 300 x 25 = 7500 lbs

Thus,

Since 7500 lbs is over the maximum capacity of 4000lbs,

The probability is 1.00
(It will definitely be 100% over the capacity)

I don't know how to solve (b) though. If you do, do share with me,