15 pts.) An industrial engineer wants to determine the average amount of time it takes an adult to assemble an "easy-to-assemble" toy.

Assuming based on prior experiences that the population variance is 36 minutes, how many observations engineer collect in order to obtain a 95% confidence estimate with a margin of error not larger than 4 minutes? Assuming the population variance is unknown, the engineer collects assembly times on sixteen (16) adults. The sample produces a mean of 20.15 minutes with a standard deviation of 5.84 minutes. What is a 95% confidence estimate for the population parameter of interest? Be sure to include an interpretation of your result. What would need to be true for you results in part B to be statistically valid?