For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of $515$ and a standard deviation of $175.$ The grading process of this year's exam has just begun. The mean score of the $40$ exams graded so far is $526.$ What is the probability that a sample of $40$ exams will have a mean score of $526$ 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.