The distribution of students' ages in your school (college, or university) is approximately normal with a population average of 26.8 years and a standard deviation of 2.5 years. a. In what percentile is the age of your 24-year old friend? Round up to the next percentile b. What is the probability that a randomly selected student is between 22 and 26 years of age? Round to four decimal places c. Calculate the minimum age of a student in the 66th percentile of the age distribution. Round up to the next whole yeard. If a sample of 35 students is randomly chosen from your school, calculate the probability that the sample average will be less than 27 years old. Round to four decimal places e. In your school, the population proportion of students who live on campus is 0.21. If a sample of 56 students are randomly selected, calculate the probability that between 20% and 44% of the students are on-campus residents. Round to four decimal places f. Sherri is one of your classmates who seriously doubts your estimate that the average age of students in your school is 24 years old. She randomly chooses five students from each of her four classes and collects their ages. Her sample average is 27 years old, with a standard deviation of3.8 years. Using Sherri's sample statistics, create a 95% confidence interval to estimate the average age of students in your school. 22 O Ho : u # 22; H1 : M = 22You will be performing the analysis by using: O The z-test with a = 0.99 O The student's t-test with a = 0.99 O The z-test with a = 0.01 O The student's t-test with a = 0.01The critical value for your analysis is O ta = :2.500 O In = 2.500 O za = 2.500 O tar/2 = $2.069 Select the correct choices for the following brief summary for Adenrele to help him understand what you have done. Using a random sample of (click to select) V students, I tested the Executive council's assertion that the average age of students in our school is (click to select) and I found that there is (click to select) to reject the null hypothesis. The council should (click to select) V their assertion that the average age of students in my school is less than 22 years