3. Central Limit Theorenl Twenty students from 3 statistics class each collected a random sample of times on how long it took students to get to class from their homes. All the sample sizes were 30. The resulting means are listed. (10 pts.) Student Mean Std. Dev. Student Mean Std. Dev. 1 22 3.7 11 27 1.4 2 31 4.6 12 24 2.2 3 18 2.4 13 14 3.] 4 27 1.9 14 29 2.4 5 20 3.0 15 37 2.8 6 17 2.8 16 23 2.7 7 26 1.9 17 26 1.8 8 34 4.2 18 21 2.0 9 23 2.6 19 30 2.2 10 29 2.1 20 29 2.8 a. The students noticed that everyone had different answers. If you randomly sample over and over from any population, with the same sample size, will the results ever be the same? b. The students wondered whose results were right. How can they nd out what the population mean and standard deviation are? c. Check the mean and standard deviation of the means. How do these values compare to the students' individual scores? d. Is the distribution of the means a sampling distribution? e. Check the sampling error for students 3, 7, and 14. f. Compare the standard deviation of the sample of the 20 means. Is that equal to the standard deviation from student 3 divided by the square of the sample size? How about for student 7, or 14