For questions 3 -5, consider that the 2012 U.S. Pet Ownership and Demographics S
ID: 3042107 • Letter: F
Question
For questions 3 -5, consider that the 2012 U.S. Pet Ownership and Demographics Sourcebook reports that 36.5% of American households have a pet dog and 30.4% have a pet cat. 3. Does it follow from this information that 66.9% (the sum of 36.5% and 30.4%) ofAmerican households have a pet dog or a pet cat? Explain/justify your answer 4. Based on the information given, what is the smallest possible value for the percentage of American households that have a pet dog or a pet cat? 5. Describe the circumstance in which this smallest possible value (from #4) would be attained.Explanation / Answer
3) No it does not follow that 66.9% households will have pet dog or pet cat. As there might be some households who had both pet dog as well as pet cat, and in such a case will be counted twice in the above servey.
4) As having a pet dog is independent of having a pet cat. So Probability of having both pet dog as well as pet cat is
0.365*0.304=0.11096
Hence the smallest probability of having a pet dog or a pet cat is
0.365+0.304-0.11096=0.55804.
Hence the smallest percentage is approximately 55.80%.
5) Such a smallest percentage is possible only when people have both pet dogs as well as pet cats.