This is from my calculus PSET
4. (Exploratory you will get full credit for these questions as long as you make a serious attempt and you turn in evidence of your thought process.) (a) Imagine you're in charge of Math 1b, and you need to get copies of the Techniques IIIest printed. At the course meeting, the TFs for the four sectionsm tell you: \"My section has about 2|] studentsr\" \"Mine's got a little under 30.\" \"I also have around 30.\" \"I've got about 20.\" How many copies of the test should you print to be sure that you'll have enough? WRITE your answer down now and don't change it later! (b) Write a sentence or two describing the strategy you used to determine how many tests to print. (UYes, there are seven sections. But we're pretending1 so let's make it a little easier. (c) The actual number of students in each of the Math 1b sections is 24, 29, 34, 23. Did you print enough tests? If not, what went wrong? What would be a better strategy to use to guarantee that you would have enough tests? Would the strategy you describe in this part or in the previous part work if there were many more sections? Please explain. {d} In the next few topics in Math 1b, one of the big ideas that we'll grapple with is the idea of bounding. In the previous parts, you should have found an upper bound for the number of tests that you'll need. This is almost certainly NOT the exact number of tests needed, but it is a number that is denitely bigger than the number of tests, while still being a reasonable value. Notice that sometimes when you're nding an upper bound, you need to do both estimation and approximation. But nding on. upper bound is not the some as estimating. Explain why someone who says \"I should print about 100 tests\" is giving a reasonable estimate but not. a reasonable upper bound for the number of tests. When we are asking you to estimate or to nd upper bounds in Math 1b we will often say \"Please be practical\" or What we mean is the following: 0 Don't say 'you should print a million tests\". Even though this is actually a valid upper bound, it's not a very useful one in this case the printer would need to run nonstop for more than 2 days! 9 Don't say \"you should print 142.734 tests\". Even though this is a valid upper bound, it's not practical to print 0.734 of a test. For that matter, it's really not any easier to print 143 tests than 150 tests: it takes only about 3|] seconds to print the extra 7 tests, so you might as well just say \"you should print 150 tests\". (e) Explain the difference between an upper bound and an estimate for the three quantities listed be low. Choose which [upper bound or estimate) would be the best response in the below scenarios. If an exact quantity is absolutely necessary, please note thatl i. Your catsitter wants to lmow how much your cat eats for dinner. ii. A researcher is trying to determine the number of experimental trials necessary for her results to reach a particular level of statistical signicance. iii Your friend wants to know how much cash they should take with th- to buy ice cream for
