In: Statistics and Probability
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 is 10.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510 . In answering the questions, use ? ‑scores rounded to two decimal places.
a) If you choose one student at random, what is the probability that the student's score is between 505 and 515 ?
b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score ?¯ ?