Problem 01 Standard Deviation Estimation [2 points] State a rule that can be used to estimate the standard deviation of a data set. Problem 02 Chebyshev's Theorem [6 points] Suppose a distribution has mean u = 17.4 and standard deviation 6 = 3.2. Without using a calculator, what does Chebyshev's Theorem tell us about the probability that a randomly selected value is between 11.0 and 27.0? Show your work answer to three decimal places Problem 03 z-Scores [5 points] Show your work answer z-scores to 2 decimal places a) You have taken the SAT and scored 400 in the verbal section of the test. Calculate a zscore to determine how good your score is compared to the general population of test takers. The population mean (u) is 469 and the population standard deviation (0') is 119. b) You have also taken the GRE and scored 500 in the verbal section of the test. Calculate a z- score to determine how good your score is compared to the general population of test takers. The population mean (u) is 590 and the population standard deviation (6) is 188. (c) In which standardized test did you perform better? Why