512.8) %3DEnter your answer as a number accurate to 4 decimal places.If 15 students are randomly selected, find the probability that their mean score is at least 512.8.P(X > 512.8) =Enter your...

Extracted text: Scores for a common standardized college aptitude test are normally distributed with a mean of 480 and a standard deviation of 106. Randomly selected students are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect. If 1 student is randomly selected, find the probability that their score is at least 512.8. Р/X> 512.8) %3D Enter your answer as a number accurate to 4 decimal places. If 15 students are randomly selected, find the probability that their mean score is at least 512.8. P(X > 512.8) = Enter your answer as a number accurate to 4 decimal places. Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help students perform better on the test. If the random sample of 15 students does result in a mean score of 512.8, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that it is possible by chance alone to randomly select a group of students with a mean as high as 512.8. O Yes. The probability indicates that it is (highly?) unlikely that by chance, a randomly selected group of students would get a mean as high as 512.8.