Q1. Suppose a random variable X ~ N( = 8, 2 = 36). Based on a sample of 36 observations, you found that sample average X = 7.5.

a) What is the sampling distribution of X ? [Hint: Central Limit Theorem]

b) How does an increase in sample size, say from 36 to 64, affect the sampling distribution of X ? Do you prefer to have a bigger sample size? Explain.

c) What is the probability of obtaining an X = 7.5 or less given the sample size is 36? Write a piece of R code to find this probability.