Relative position measures Instructions: In this task, we will work with relative position measures, the empirical rule and Chebyshev's theorem. You will calculate relative position measurements and use the rule of thumb in various situations. You should present the necessary processes to support the response of the exercises and round the final results-not the intermediate values that appear during the calculations-to two decimal places, when necessary. Question #1 1) The weight of a group of nursing students has a normal distribution, with an average of 148 pounds and a standard deviation of 22 pounds. If you use the rule of thumb, what is the approximate percentage of students between: a) 104 and 192 pounds, b) 82 and 214 pounds? (3 points) Question #2 1) The average height of men is 69 inches and their standard deviation is three (3) inches. Carlos is 65 inches tall (Triola, 2004). Answer me: a) What is the difference between Carlos' height and the average? (1 point) b) How many standard deviations from the mean is approximately Carlos' height? Use the rule of thumb to answer this question. (2 points) c) Turn Carlos' height into a Z-score. (2 points) d) If we consider that the "common" heights are those that correspond to Z- scores between -2 and 2, is Carlos' height common or uncommon? (2 points) Question #4 1) Which is relatively better: a score of 88 on a psychology exam or a score of 45 on an economics exam? Psychology test scores have a mean of 92 and a standard deviation of 10. Economics exam scores have a mean of 57 and a standard deviation of 5. Use relative position measures to answer this exercise (Z-score) (Triola, 2004). (3 points) Question #5 1) What is the highest relative score of the three (3) scores below? Use the Z-value to answer. (3 points) a) a test score of 194 with a mean of 128 and a standard deviation of 34 b) a score of 91 on a test with a mean of 86 and a standard deviation of 18 c) a score of 17 on a test with a mean of 15 and a standard deviation of 5 Question #6 1) In a time study conducted at a manufacturing plant, the time to complete a specified operation was measured for each of the 40 workers. The mean and standard deviation were found to be 14.8 and 1.6, respectively. Describe sample data using the rule of thumb (Mendenhall et al., 2015). (3 points) Question #7 1) The mean and variance of a sample of 25 data items are 78 and 100, respectively. Use Chebyshev's theorem to describe the distribution of data. (3 points) Question #3 1) With an average of 98.20 and a standard deviation of 0.62, it converts the following temperatures into Z-scores. a) 97.52 (2 points) b) 98.60 (2 points) c) 98.10 (2 points) Question #8 1) The data below are the weights (in pounds) of 15 packets of ground beef in refrigerators from the Supermax supermarket: 1.28, 90, 1.29, 1.15, 93, 1.18, 89, 1.12, 2.33, 1.94, 2.14, 2.6, 1.11, 1.9, 1.2 (Mendenhall et al., 2015). a) Construct a stem and leaf graph to show the distribution of those weights. (3 points) b) Find the mean and standard deviation of the data set. (4 points) c) Find the percentage of measurements in the intervals of the rule of empirical rule. (3 points)