to study the grades of mathematics for the UGRU students, a sample of 25 students where randomly selected and sample average was 82 points and the sample standard devotion was 10 points , if the grades of mathematics for the UGRU students distributed normally .

a)find a 99% confidence intreval for the true mean of the grades of mathematics .

b)what sample size should be taken so that a 99% confidence intreval will have a margin error less than 3 points and standard devation 10 points