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)Whats 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 their cat?
D)What concerns do you have?

Thank you!!

To answer these questions, we will use basic principles of probability and statistics. Here's how to solve each part:

A) The expected difference in the cost of medical care for dogs and cats can be found by subtracting the average cost for dogs from the average cost for cats. So, the expected difference is $120 - $100 = $20.

B) To find the standard deviation of the difference, we need to use the formulas for combining variances. The variance of the difference between two random variables is equal to the sum of their variances. Since the standard deviation is the square root of the variance, we can compute the standard deviation of the difference using the formula:

Standard deviation of the difference = sqrt((Standard deviation of dogs)^2 + (Standard deviation of cats)^2)
= sqrt($30^2 + $35^2)
= sqrt(900 + 1225)
= sqrt(2125)
= $46.09

Therefore, the standard deviation of the difference in cost between dogs and cats is approximately $46.09.

C) If we assume that the costs follow a normal distribution, we can compare the z-scores corresponding to the difference in costs. The z-score for a particular value in a normal distribution tells us how many standard deviations that value is from the mean. Since we are interested in the probability that medical expenses are higher for someone's dog than for their cat, we can calculate the z-score using the formula:

z = (x - μ) / σ

Where x is the desired cost (in this case, $0), μ is the expected difference ($20), and σ is the standard deviation of the difference ($46.09).

Using the z-score table or a calculator, we can find the probability associated with the z-score. In this case, we want the probability of a dog's medical expenses being higher than a cat's, so we need to find the probability to the right of the z-score.

D) As a bot, I don't have concerns, but with statistical analysis, it is important to ensure the assumptions made for the calculations are valid. In this case, assuming the costs follow a normal distribution might not hold true in the real world. It's also crucial to consider the sample size and whether it accurately represents the population as a whole.

Additionally, it is important to note that these calculations are based on averages and do not take into consideration individual variations. The actual costs for individual dogs and cats can vary significantly.

It is always a good practice to critically evaluate the assumptions, data, and methods used in statistical analysis.

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