SOLUTION: A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 298 lb. and a variance of 2500. (Give your answers correct to four

Question 875040: A trucking firm delivers appliances for a large retail operation. The packages (or crates) have a mean weight of 298 lb. and a variance of 2500. (Give your answers correct to four decimal places.)
(a) If a truck can carry 4120 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 7860 lb., what is the probability that it will be able to carry the entire lot of 26 appliances?

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
mean weight of 298 lb. and a variance of 2500, sd = 50
Re: TY, sry typo
a) 4120/26 = 158.4615,
Sample: 26
P(x > 158.4615), z = (158.4618-298)/50/sqrt(26) = -139.5385/9.8= -14.2386
P(z > -14.2386) = basically a 100% chance of aggregate weight greater than the truck's capacity
b) 7860/26 = 302.3
P(x > 302.3), z = 4.3/9.8 = .4388
P(z > .4388) = .3304 0r 33.04% chance of aggregate weight greater than the truck's capacity
Below: z = 0, z = � 1, z= �2 , z= �3 are plotted.
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right

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