A shipping company handles containers in three different sizes . 27 ft3 (3 x 3 x

Question

A shipping company handles containers in three different sizes . 27 ft3 (3 x 3 x 3) 2. 125 ft3 3. 512 ft3 Let x, ( 1, 2, 3) denote the number of type i containers shipped during a given week. with .-E(X) and ? = V(X), suppose that the mean values and standard deviations are as follows M1 = 400 2 = 450 3 = 50 1 = 8 2 = 10 3 = 12 Suppose that the X'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.) You may need to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

expected value of volume is 27(400) + 125(450) + 512(50)=92650.
variance of volume is (27)^2(8)^2 + (125)^2 (10)^2 + (512)^2 (12)^2 = 39357892

std.dev = sqrt(variance) = 6273.587

P(x < 100000)

z = (x - mean) / s

= (100000 - 92650) / 6273.587

= 1.1715

P(X < 100000) = P(z < 1.1715)= 0.8793 by using standrad table

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