A public administration student wants to determine the average amount that the members of the city councils of the big cities earn per month as remuneration. 

a) The error in estimating the mean must be less than $ 100, with a 95% confidence interval. The student found a report from the Department of Labor that the standard deviation is calculated at $ 1,000. What is the required sample size? 

b) If the student wants to increase the confidence level, for example, to 99%, how much will the sample size be?