In Iowa many farms have their own silos for holding corn At

In Iowa, many farms have their own silos for holding corn. At a specific farm with one silo, the capacity for the silo is 12,000 bushels of corn. During harvest, each wagon is filled and the corn from the wagon is placed in the silo. The amount of corn in each wagon is normally distributed with a mean of 300 bushels and a standard deviation of 30 bushels (the variability is due to machine operator). Wagons are independent of each other. What is the probability that when 39 wagons of corn are emptied into the silo, that the silo will be above capacity?

Solution

capacity = 12,000 39 wagons: 12,000/39 = 307.6923 per wagon If mean of 39 wagson is above 307.6923, then the silo will be above capacity. Distrubtion of sample mean: mean = 300 standard deviation = 30/square root of 39 = 4.8038 Z score: (307.6923 - 300)/4.8038 = 1.6013 P(mean > 307.69) = P(Z > 1.6013) = 1 - P(Z < 1.6013) = .0547 ANswer: .0547