Pets (Extra Credit) The American Veterinary Association claims that the annual c

Question

Pets (Extra Credit)

The American Veterinary Association claims that the annual cost of medical care for dogs averages $ I00, with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35.

What's the expected difference in the cost of medical care for dogs and cats?

What's the standard deviation of that difference?

If the costs can be described by Normal models, what’s the probability that medical expenses are higher for someone’s dog than for her cat?

What concerns do you have?

Explanation / Answer

Expected difference in the cost of medical care for dogs and cats = 100-120 = -20

Var of difference = Var(X-Y) = Var(x)+Var(Y)

= 900+1225 = 2125

Std dev = square root 2125 = 46.10

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P(X>y) = P(Diff>0) = P(Z>20/46.10)

=P(Z> 0.43)

= 0.5-0.1664

= 0.3336

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