Americans spend billions on veterinary care each year. According to the APPA National Pet Owners Survey, U.S. citizens spent $10.1 billion on pet care in 2007. The health care services offered to animals rival those provided to humans, with the typical surgery costing from $1700 to $3000 or more. On average, a dog owner spent an estimated $670 on veterinary-related expenses in that year. Source: American Pet Products Manufacturers Association Assume that annual dog owner expenditure on health care is normally distributed with a mean of $670 and a standard deviation of $290.
a. What is the probability that a dog owner, randomly selected from the population, spent over $1000 in health care in 2007?
b. Suppose a survey of 300 dog owners is conducted, and each is asked to report the total of his or her vet care bills for 2007. What is the probability that the mean annual expenditure of this sample falls between $700 and $750?
c. The assumption of a normal distribution in this situation is likely misguided. Explain why and what effect this had on the answers to parts a and b.