assume that in 2018 the mean mathematics sat score was 536 andthe standard deviation was 115. a sample of 68 scores is chosen. a)what is the sampling distribution of *? b) what is the probabilitythe sample mean score is less than 510? c) what is the probabilitythe sample mean score is between 485 and 525? d) what is theprobability the sample mean score is greater than 480? e) would itbe unusual for the sample mean to be greater than 575? show work toprove your answer.