(Solved): Scores for a common standardized college aptitude test are normally distributed with a mean of 512 ...

Scores for a common standardized college aptitude test are normally distributed with a mean of 512 and a standard deviation of 111. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect. If 1 of the men is randomly selected, find the probability that his score is at least \( 574.9 \). \( P(X>574.9)= \) Enter your answer as a number accurate to 4 decimal places. If 9 of the men are randomly selected, find the probability that their mean score is at least \( 574.9 \). \( P\left(M>\frac{1}{574.9)}=\right. \) Enter your answer as a number accurate to 4 decimal places.