Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score u 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 is 510. Macmillan Learning If you choose one student at random, what is the probability that the student's score is between 505 and 515? Use Table A or software to calculate your answer. Give your answer to four decimal places. probability: 1

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 10.4 Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 495.   © Macmillan Learning Using the same sample size of 25 students, what is the probability that the mean score of your sample is between 490 and 500? Give your answer to four decimal places. What is the 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 from a statistical study of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.1. Suppose that the typical mean score of those taking the MCAT on your campus has been equal to 25. (a) If you choose one student at random, what is the probability that the student's score is between 20 and 30? (Round your answer to four decimal places.) (b) You sample twenty-five students. What is the standard deviation of sampling distribution of their average score x? (Enter your answer to two decimal places.) (c) What is the probability that the mean score of your sample is between 20 and 30? (Round your answer to four decimal places if needed.)

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 2.7 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. Solve the problem using the critical region method of testing (i.e., traditional method). (Round the your answers to three decimal places.)   test statistic =   critical value =   State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average fish length is less than 19 inches.Reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches.    Fail to reject the null hypothesis, there is…