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A shipping company handles containers in three different sizes.

A shipping company handles containers in three different sizes. 

1. 27 ft3 (3 x 3 x 3) 

2. 125 ft3

3. 512 ft3 


Let Xi (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With μi = E(X;) and σi2 = V(Xi), suppose that the mean values and standard deviations are as follows. 

μ1 = 500 μ2 = 450 μ3 = 50

σ1 = 8    σ2 = 12    σ3 = 10  


Suppose that the Xi's are independent with each one having a normal distribution. What is the probability that the total volume shipped is at most 100,000 ft3 (Round your answer to four decimal places.)

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