In: Math
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.)