Problem #1 NOTE: For all problems in this assignment, do NOT use the empirical rule unless specifically told to do so. Instead, use R for more precise calculations. A construction company wishes to predict the amount of concrete that was needed to fill 4x4 meter patios. By reviewing other patios of similar areas, drainage patterns, etc., they note that the volumes (in cubic feet) were approximately normally distributed: N(24.3, 4.8) For this problem, answer all questions to 1 decimal place unless specified differently in a particular question. 1. In one to two paragraphs, and in your own words, describe what is meant by standard deviation. Note: | do nof want a mathematical explanation. Rather, | want you to explain in words what the standard deviation is. You can include numbers if you need them to help with your discussion, but | do not want to see the actual formula for SD. This question is worth up to 3 points. You will be given full points based on your ability to convince the grader that you do indeed understand the concept of SD. Note: You may be asked to do this again on one of your exams.... 2. What percentage of patios would be expected to require less than 20 cubic feet? Hint: Remember that R's pnorm( ) function gives the area to the left under the density curve. One patio required 35.2 cubic feet. Would percentile would this correspond to? How much volume would be required to be at exactly the 33rd percentile? 5. A profit can be made as long as the volume is less than 32 cubic feet, whereas if it takes more than 32 cubic feet, it will probably result in a loss. What percentage of patios will result in a LOSS? 6. What percentage of patios would require between 28 and 32 cubic feet? What percentage of patios have a volume with a z-score of less than -1.3? 8. What percentage of patios have a volume with a z-score of more than +1.5? & W o~