# Statistics HW

Suppose you are interested in adopting a Yorkie Poo, but our apartment complex has weight requirements that must be met for all dogs owned by residents. Based on you research, it seems that the average weight of all Yorkie Poos, ????, is 10 pounds with standard deviation, ????, 1.67 pounds.  a. Completely specify the distribution of a random Yorkie Poo (X).  b. What is the probability that a Yorkie Poo will weigh between 9 and 11 pounds? c. Your apartment requires that all dogs be less than 18 pounds. Is it likely that this breed will not be larger than 18 pounds? d. Completely specify the distribution of the average weight of a group of 16 Yorkie Poos (????̅). e. What is the probability that the average weight of a group of 16 Yorkie Poos is between 9 and 11 pounds f. Find and interpret a 90% confidence interval for the mean weight of Yorkie Poos given the following weights of a random sample of 5 Yorkie Poos: {8.1, 6.7, 7.9, 11.2, 10.9}. Use ????=1.67 pounds. g. Without performing any calculations, would you expect a 95% confidence interval for the mean weight of Yorkie Poos to be larger or smaller than the 90% confidence interval you constructed in part (f)? h. Assume we don’t know ????. Construct a 90% confidence interval for the mean weight of Yorkie Poos given a sample consisting of the same 5 dogs in part (f): {8.1, 6.7, 7.9, 11.2, 10.9}.

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