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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
27.  A shipping company handles containers in three dif- ferent sizes: (1) 27 ft3 (3 X 3 X 3), (2) 125 ft3, and
(3) 512 ft3. Let Xi (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With
mi  = E(Xi) and s2  = V1X 2 , suppose that the mean
Â
29.  Five automobiles of the same type are to be driven on a 300-mile trip. The rst two will use an econ- omy brand of gasoline, and the other three will use a name brand. Let X1, X2, X3, X4, and X5 be the ob- served fuel ef ciencies (mpg) for the ve cars. Sup-
Â
i                  i
Â
values and standard deviations are as follows:
Â
|
m1 = 200 |
m2 = 250 |
m3 = 100 |
|
s1 = 10 |
s2 = 12 |
s3 = 8 |
a.   Assuming that X1, X2, X3 are independent, calculate the expected value and variance of thepose these variables are independent and normally distributed with m1 = m2 = 20, m3 = m4 = m5 = 21, and s2 = 4 for the economy brand and 3.5 for the name brand. De ne an rv Y by
Â
X1 + X2Â Â Â Â Â Â Â Â Â Â Â X3 + X4 + X5Â Y =Â Â -
Â
total volume shipped. [Hint: Volume = 27X1 +Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3
125X2 + 512X3.]
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b.  Would your calculations necessarily be correct if the Xi s were not independent? Explain.
so that Y is a measure of the difference in ef ciency
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between   economy   gas   and   name-brand   gas. Compute P(0 Y) and P(-1 Y 1). (Hint: Y =
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