Pets. The American Veterinary Association claims that the...

Pets. The American Veterinary Association claims that the annual cost of medical care for dogs averages $\$ 100$, with a standard deviation of $\$ 30$, and for cats averages $\$ 120$, with a standard deviation of $\$ 35$. a) What's the expected difference in the cost of medical care for dogs and cats? b) What's the standard deviation of that difference? c) 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? d) What concerns do you have?

Transcript

00:01 So we have information for dogs and for cats, and the mean expense for the dogs is $100, and the standard deviation for the dog is $30.

00:13 And interestingly enough, we have the mean for the cats is equal to 120, and the standard deviation for the cats is $35.

00:21 And we want to look at the difference between the two, and i'm going to let d stand for difference, the random variable d, and i'm going to take the dog.

00:30 Minus the cat data.

00:32 So that's how my difference will be.

00:34 And your first question asked, what would be the expected value of d? and that expected value would be, or the average is the mean of d.

00:47 And that's going to be to subtract literally the means of those two appointments.

00:52 And so that is negative $20.

00:55 So you would anticipate that the difference would be a negative value.

00:59 And then you want to know what the standard deviation is of the difference.

01:03 Well the standard deviation when we find the difference of variables is we have to add their variances and which is not necessarily intuitive but that's what happens.

01:13 So we take that 30 squared plus the 35 squared and underneath the radical that would be the variance and so the standard deviation is going to be that square root of 900 plus i don't know what 35 squared is i could click multiply it but just use my calculator and find it.

01:30 That comes out to be 46 .09 and i'll call it $8.

01:36 Now on part c we want to look at what is the likelihood that the dog would cost more than the cat and that means that we want the difference to be greater than zero and we're supposed to assume a normal model and so we would convert this to a z value and this is our mean and this is our standard deviation so we would take that zero minus negative 20.

02:04 And i quick draw a picture here as well.

02:08 If we're down here at negative 20, what's the likelihood of getting a zero or higher? so that zero with a standard deviation of 46, 40, you know, this would be about at 20...

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