What are the answers for the problems below? please give me explanations as well. please ignore the red number. thank you

Part lll: AP Statistics Practice Tests 13. 14. 15. The weekly milk output of a population of Guernsey cows is normally distributed with population mean [ = 40 quarts and standard deviation 6 = 12 quarts. A sample of 36 cows is taken, and the sample mean X is computed. What is the mean and standard deviation of X7 A. [y=40 quarts, G ,= |12 quarts B. =40 quarts, 6, =2 quarts C. W;=40 quarts, 6 ; ="/, quart D. u.=6%qunns.c. = 12 quarts E. ;=6 % quarts, 6 ; = 2 quarlts The students in a large school district are taking a standardized geography exam that is constructed to have a standard deviation = 20. The school district wants to create a 99% confidence interval for the true mean score on this exam, for the students in their district. They also desire that the width of the interval be no greater than five units wide, Approximately how many students in the district should be sampled in order to create this confidence interval? A. 25 B. 110 C. 250 D. 350 E. 425 Suppose that a prestigious law school, as a policy, accepts only a percentage of applicants for admission. Let p represent that percentage. If 80 random applicants were polled, and 28 of those applicants indicated that they were accepted to the college, what would be a 90% confidence interval for p? A, 0.3500 % 0.0047 B. 0.3500 0.0533 C. 0.3500 0.0694 D. 0.3500 + 0.0877 E. 0.3500 0.1045 16. Samantha has taken the first two exams in her 17. 18. Calculus class. She scored 78 on the first exam and 84 on the second exam. The class average on the first exam was 70, with a standard deviation of 10. The class average on the second exam was 75, with a standard deviation 17. Which statement describes how well Samantha did on the two exams, relative to the rest of the class? A. Samantha did better on the first exam. B. Samantha did better on the second exam. C. Samantha did equally well on both exams. D. How well she did cannot be determined, because the sample size is not given, E. How well she did cannot be determined, because it is not known whether the sample sizes were the same on both exams. Suppose that the distribution of a set of values has a population mean of 76 and a standard deviation 14. If 6 is subtracted from each score and then cach score is divided by 2, what will be the new mean and standard deviation of the set of values? A. Mean = 76; standard deviation = 14 B. Mean = 70; standard deviation = 14 C. Mean = 70; standard deviation = 7 D. Mean = 35; standard deviation = 14 E. Mean = 35; standard deviation = 7 Suppose that it has been determined that 16% of all homes with washing machines have Brand A, while 12% of all homes with washing machines have Brand B. Also, 2% of homes with washing machines have both brands. If six homes that have washing machines are selected at random, what is the approximate probability that none of these homes will have either Brand A or B? A. 0.003 B. 0.139 C. 0.164 D. 0.260 E. 0740