You draw a sample of size 50 from a normally distributed population with a known standard deviation for the population of four.

a. What is the standard error of the sample mean in this scenario, rounded to two decimal places? (1 mark)

b. What is the distribution of the sample mean? (1 mark)

c. If you want to construct a two-sided 95% confidence interval, how much probability will be in each tail of the distribution? (1 mark)

d. What is the appropriate z-score for a 99% confidence interval for this data? (1 mark)

e. Rounding to two decimal places, what is the 99% confidence interval if the sample mean is 51? (1 mark)

f. For any given data set and sampling situation, which would you expect to be wider: a 95% confidence interval or a 99% confidence interval? (2 marks)