1.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/gmatscoring-by-exam-section-normal-view#tab5).

(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)