Question: Pure-bred dogs competing in shows must often meet specific height criteria to be within the breed standard. A new breed of dog, the pug-cock-a-poo, has been approved by a kennel club. To establish the breed standard, the organization of breeders has taken the height from a sample of 25 pug-cock-a-poos and found the sample mean to equal 14 inches. The variance of this sample is 2.25.

a. Construct a 90% confidence interval for the population mean height of the pug-cock-a-poos. b. What assumption is necessary for constructing the aforementioned interval?