The birthweights for babies born at 40 weeks follow a normal distribution with mean 3.46kg, and a standard deviation 0.58kg.
(a) What is the expected total weight of 100 randomly chosen babies?
(b) What is the standard deviation of the total weight of 100 randomly chosen babies?
(c) Repeat parts (2a) and (2b) for the average weight of 100 randomly chosen babies.
(d) What is the expected total weight of 10,000 randomly chosen babies?
(e) What is the standard deviation of the total weight of 10,000 randomly chosen babies?
(f) Repeat parts (2d) and (2e) for the average weight of 10,000 randomly chosen babies.
(g) Using your answers to the earlier parts of this question, explain how the sample size a ects the mean and SD of the sum of a collection of random variables. Limit your answer to 2-3 sentences.
(h) Using your answers to the earlier parts of this question, explain how the sample size a ects the mean and SD of the average of a collection of random variables. Limit your answer to 2-3 sentences.
(i) In 2-3 sentences, explain the connection between your answer to part (2h) and the phenomena seen in Q2(k) from Homework 3 (about how `certain' you were in your estimate given 1000 months of data rather than just 100, see the HW3 solutions for details).