Almost all medical schools in the United States require studentsto take the Medical College Admission Test (MCAT). To estimate themean score μ μ of those who took the MCAT on your campus, you willobtain the scores of an SRS of students. The scores follow a Normaldistribution, and from published information you know that thestandard deviation is 10.4 . Suppose that, unknown to you, the meanscore of those taking the MCAT on your campus is 500 . In answeringthe questions, use z ‑scores rounded to two decimal places. (a) Ifyou choose one student at random, what is the probability that thestudent's score is between 495 and505 ? Use Table A, or software tocalculate your answer. (Enter your answer rounded to four decimalplaces.) probability: (b) You sample 25 students. What is thestandard deviation of the sampling distribution of their averagescore x¯ ? (Enter your answer rounded to two decimal places.)standard deviation: (c) What is the probability that the mean scoreof your sample is between 495 and 505 ? (Enter your answer roundedto four decimal places.) probability:
