Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information, you know that the standard deviation of scores for all MCAT takers is 10.8. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is510.

Using the same sample size of 36 students, what is the probability that the mean score of your sample is between 505 and 515?

Give your answer to four decimalplaces.