Question

A shipping company handles containers in three different sizes. 

1. 27 ft³ (3 x 3 x 3) 

2. 125 ft³

3. 512 ft³ 

Let X_i (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With μ_i = E(X;) and σ_i² = V(X_i), 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 X_i'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.)

Answer 1