Question: In order to gain acceptance to a medical school, a prospective medical student must take (and do well on) a standardized test called the MCAT. The test has four parts, three of which (physical sciences, verbal reasoning, biological sciences) are multiple choice tests whose scaled scores have range 1 to 15 and mean 8. The standard deviation for each of these three sections is 2. The random variables assigning scaled scores on the three parts are all normal distributions. (The fourth part is a writing sample and is not graded on the same sort of scale. We do not consider this part in this question.)

? Assuming the three random variables P (assigning scaled score on the physical sciences part), V (assigning verbal reasoning scores), and B (assigning biological sciences scores) are independent, what are the mean and standard deviation of the random variable T = P + V + B assigning total score on the three parts?

? Generally, a total score of at least 30 is needed (along with a high gpa) for admission. What proportion of the students taking the exam would be expected to score 30 or higher?

? If Tbar is the distribution of all sample means from samples of size 9 drawn from T, what are the mean and standard deviation of Tbar?

? If the about to graduate group of 9 aspiring medical students at Big State U average a total of 25.5, would that suggest this school has a stronger pre-med program than average? Explain.