Please include workings out

Question 1 a} The average income of a country ('Bull-a-stan') is known to be equivalent 10,000 with standard deviation 1,250. A sample of 50 workers is taken and their average income calculated. i} What is the probability distribution of this sample mean? ii} What is the probability of the sample mean being over 10,250? iii) What is the probability of the sample mean being below 9,500? iv] If the sample size were 10. why could you not use the same methods to find the answers to (i) (iii)? (20 marks)