Exercise 2

1. Consider the population data in the file normal.txt. This data is normally distributed.
   1. Find the population mean and variance
   2. Generate a random sample of size 50. (i.e. randomly select 50 numbers from the population). Find a 90% and 95% confidence interval for the mean. Is the population mean within the intervals?
   3. Generate a random sample of size 10. (i.e. randomly select 10 numbers from the population). Find a 90% and 95% confidence interval for the mean. Is the population mean within the intervals?
2. Repeat the exercise above for the population data in the file not-normal.txt. This data is not normally distributed. For the smaller sample (size 10), compute the confidence intervals with and without normalization.