2. A truck is loaded with 900 boxes of books. If the total weight of the boxes e

Question

2. A truck is loaded with 900 boxes of books. If the total weight of the boxes exceeds 36,450 pounds, the driver will be fined at the weighing station. Assume that the weight (W) of a (i.e. one) randomly selected box of books from the entire population of boxes of books has a mean of ,-40 pounds and a standard deviation of w-6 pounds (a) Find the probability that the driver will be fined (b) Twenty percent (20%) of the time, 900 of these boxes of books will weigh a total of at least how many pounds? What is the probability that one randomly selected box of books will weigh between 34 and 46 pounds? What is the probability that the combined weight of 5 randomly selected boxes of books will exceed 210 lbs.? (c) (d)

Explanation / Answer

a) for 900 box mean =40*900=36000

and std deviation =6*(900)1/2 =180

hence probability that driver will be fined

b) for 20% top most weight at 80th percentile ; z=0.8416

hence corresponding weight =mean +z*std deviation =36000+0.8416*180 =36151.49 pounds

c)

d)

for 5 box mean =40*5=200

and std deviation =6*(5)1/2 =13.42

for normal distribution z score =(X-)/ here mean=       = 36000.000 std deviation   == 180.00

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