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 175. The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 496. What is the probability that a sample of 40 exams will have a mean score of 496 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.