Refer to Exercise 58, and 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?
Reference Exercise 58;
A shipping company handles containers in three different sizes: , suppose that the mean values and standard deviations are as follows:
a. Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume + 27X1 + 125X2 + 512X3.]
b. Would your calculations necessarily be correct if the Xi’s were not independent? Explain.
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