Almost all medical schools in the United States require studentsto take the Medical College Admission Test (MCAT). To estimate themean score ?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 10.8. Suppose that, unknown to you, the meanscore of those taking the MCAT on your campus is 495.
In answering the questions, use z‑scores rounded to two decimalplaces.
(a) If you choose one student at random, what is the probabilitythat the student's score is between 490 and 500? (Enter your answerrounded to four decimal places.)
(b) You sample 36 students. What is the standard deviation ofthe sampling distribution of their average score x¯ ? (Enter youranswer rounded to two decimal places.)
(c) What is the probability that the mean score of your sampleis between 490 and 500? (Enter your answer rounded to four decimalplaces.)
