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Combining Random Variables: A Van Full of Characters -

APSTAT-3TGJXI

Homer Simpson has yet another new job. He is now the personal chauffeur for a bunch of characters. These characters always travel together to places like the Cartoon-Con Convention, and Homer always drives them in a van that weighs $4050$ pounds.

Of course, Homer's weight and the weights of the other characters go up and down a bit each day depending on how much they have been enjoying their food. The table below gives Homer's and each of the other character's mean weights and the standard deviation of their weights (in pounds).

Mean Standard Deviation
Homer Simpson 225 4
Porky Pig 180 5.1
Scooby Doo 140 3.8
Donald Duck 2.7 0.4
Wile E. Coyote 35 1.2



What is the mean AND the standard deviation of the total weight of the van when Homer and all of the other characters are in transit (disregard the weight of gas, oil, and any other extras)?

A

Mean $= 582.7$ pounds
Standard Deviation $= 1.6$ pounds

B

Mean $= 582.7$ pounds
Standard Deviation $= 7.62$ pounds

C

Mean $= 4632.7$ pounds
Standard Deviation $= 1.6$ pounds

D

Mean $= 4632.7$ pounds
Standard Deviation $= 7.62$ pounds

E

We cannot find the standard deviation of the total weight since we are not given the standard deviation of the weight of the van