Based on the performance of all individuals who tested between 2015 and 2017, the GMAT total scores are normally distributed with a mean of 561.27...

Based on the performance of all individuals who tested between 2015 and 2017, the GMAT total scores are normally distributed with a mean of 561.27 and a standard deviation of 119.31. (https://www.gmac.com/gmat-other-assessments/accessing-gmat-exam-scores-and-reports/gmat-scoring-by-exam-section-normal-view#tab5). Show all work. Just the answer, without supporting work, will receive no credit. 

(a) For a sample of size 100, state the standard deviation of the sample mean (the "standard error of the mean"). (Round your answer to three decimal places) 

(b) Suppose a sample of size 100 is taken. Find the probability that the sample mean GMAT total scores is more than 575. (Round your answer to three decimal places)