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.)

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Expert Solution

milcah answered 2 years ago

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