The arithmetic test of the NAEP (National Assessment of Education Progress) survey was applied to a sample of 1,077 women between 21 and 25 years old. The average of their results was 275 points. Suppose that the standard deviation of all individual results is = 60 points.

a) Calculate a 95% confidence interval for the mean of the results of the population of young women of these ages.

b) Suppose that the same result, x = 275, comes from a sample of 250 women. Find a 95% confidence interval for the population mean in this case.