For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 505 and a standard deviation of 180. The grading process of this year’s exam has just begun. The average score of 40 the exams graded so far is 508 . What is the probability that a sample of 40 exams will have a mean score of 508 or more if the exam scores follow the same distribution as in the past?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.