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# Finite Math with Applications MATH 1313

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This 10 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1313 at University of Houston taught by Rebecca Heeth in Fall. Since its upload, it has received 484 views. For similar materials see /class/208371/math-1313-university-of-houston in Mathmatics at University of Houston.

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Date Created: 09/19/15

Math 1313 Section 62 The Number of Elements in a Finite Set Sometimes we will need to know how many elements are in a set This is obvious if our sets are all given in roster notation Usually however we ll have more work to do In this section we ll learn a rule that will help to solve problems of this type We ll start with notation Notation If A is a set then nA denotes the number of elements in the set Example 1 SupposeA 1 2 3 4 5 Find nA Example 2 Suppose B x l x is a letter in the alphabet Find nB Rules 1 HA and B are disjoint sets then nA U B nA nB 2 If A and B are not disjoint sets or if we don t know whether or not they are disjoint then nA U B nA nB 7 nA m B Why is Rule 2 true Example 3 Suppose nU l50 nA 85 nB 95 and nA m B 65 a Find nA U B b Find nA m BC Math 1313 Class Notes 7 Section 62 Page 1 of4 c Find nAc U BC d Find nAc U 13 Example 4 After an election 100 people leaving the polls were surveyed 52 said they had voted for Proposition 1 and 38 said they had voted for Proposition 2 18 said they had voted for both How many voted for neither Math 1313 Class Notes 7 Section 62 Page 2 of4 Example 5 A company advertises its products in three different magazines People Self and Cosmopolitan A survey of 125 customers showed where they learned of the products These are the results 63 from People 60 from Cosmopolitan 53 from Self 18 from People and Cosmopolitan but not Self 17 from People and Self but not Cosmo 15 from Cosmopolitan and Self but not People 14 from only Self How many customers saw ads in a at least 2 magazines b at least 1 magazine c exactly 2 magazines d exactly 1 magazine How many customers learned of the products from some other source Math 1313 Class Notes 7 Section 62 Page 3 of4 Example 6 A survey of small business owners asked whether they owned the following items for their businesses laptop computer fax machine photocopy machine The results of the survey showed that 112 business owners owned laptops 126 owned fax machines and 170 owned photocopiers Fortysix business owners owned all three types of equipment and 63 owned none of these three types of equipment In addition 84 business owners owned both laptops and fax machines 71 owned both laptops and photocopiers and 69 owned both fax machines and photocopiers How many business owners a owned a laptop but not a fax machine or a photocopier b owned exactly one of the three types of machines c owned exactly two of the three types of machines d participated in the survey Math 1313 Class Notes 7 Section 62 Page 4 of4 Math 1313 Finite Mathematics with Applications Instructor Rebecca Heeth Email Address rheethmathuhedu THIS IS NOT THE SYLLABUS The syllabus course policies class notes etc are all on my web page httpwwwmathuhedutheeth Prerequisite Math 1310 College Algebra Prerequisites will not be checked All students MUST take Test 1 If you do not score a 70 or better on Test 1 you are highly recommended to drop the course If you do not drop the course you are taking a risk in failing the course Beginning of the Semester ToDo List 1 Read the syllabus and Course Policies Departmental Policies for 13xx You are responsible for knowing these policies Read them carefully and make sure you understand all of them If you have any questions about them ask me You can nd them in one of the course packets and also on my webpage You may be asked daily quiz popper questions over these policies 2 Sign up for a CourseWare CASA account at httpwwwcasauhedu if you don t already have one First of all CASA is the name of the Testing Center where you will take all tests excluding the nal exam CASA is located at 221 Garrison GAR CourseWare is the name of the site where you will log in to take tests excluding the nal exam quizzes and practice tests You will need a reservation for each test excluding the nal exam These reservations can be made by logging into your CourseWare account If you encounter any CouseWare site problems rst make sure that you are enrolled you can t create an account if you are not enrolled then click on the Email Tech Support link on the CourseWare site Ifnothing else works go to 221 Garrison 3 Take Practice Test 1 on CourseWare Practice Test 1 will indicate what material is covered on Test 1 so it will help you get ready for Test 1 All material on Test 1 is prerequisite material 7 material you are expected to have learned in a class you took before this one We will go over this material the rst week of class You can earn extra credit points for taking Practice Test 1 You can take Practice Test 1 up to 20 times Get help on anything you39ve forgotten The Mathlab is located at 222 GAR next door to the Testing Center CASA If you score below 70 on Test 1 there is a good chance that you are in the wrong class and are at risk of failing this course 4 Take Test 1 at CASA Testing Center You will be able to make a reservation the rst week of classes Check the Academic Calendar on my website for Test l s testing period Once you log into your CourseWare account CASA account click on Proctored Tests you will see the testing period and available dates there also 5 Get your Grading ID This number is your PeopleSoft ID number also called the MyUH ID number You can nd your PeopleSoft ID number by logging into your UH online account and your CourseWare account You will need this ID number in class nearly every day so you should write it down and keep it handy 6 Locate the online text at wwwcasauhedu There is not a required bound text for this course The text is online 7 Buy scantron packets 23 and 24 at the UH Bookstore The red scantrons will be used for homework assignments Each assignment will be turned in using one and only one of these Homework will start being collected in Week 3 of the semester The purple scantrons will be used for daily inclass quizzes aka poppers Poppers will begin in the 3rd week of the semester We ll have one daily inclass quiz each class period until the last day of class 8 Take the Course Policies Quiz 0n CourseWare You must score 100 on this quiz before you can access the practice tests starting Week 1 or weekly quizzes starting week 3 on CourseWare The answers to all the questions can be found in the Departmental Policies for 13XX Math 1313 Section 86 Applications of the Normal Distribution We have reached the last section of the text that we will cover in the course This section covers some word problems involving normally distributed random variables You may notice that there is some similarity between the wording of these problems and the wording of the Cheby chev s Inequality problems You will know to use the normal distribution to solve a problem when you are told that the random variable is normally distributed Ifthose words aren t there then you are probably looking at a Chebychev s Inequality problem Example 1 According to the data released by the Chamber of Commerce the weekly wages of factory workers in a small city are normally distributed with a mean of 1000 and a standard deviation of 100 What is the probability that a randomly selected factory worker who lives in the city makes a weekly wage of a less than 900 b more than 1200 c between 850 and 1150 3 Example 2 The heights of a certain species of plant are normally distributed with a mean of 30 and a standard deviation of 3 What is the probability that a plant chosen at random will be between 24 and 32 inches tall Sometimes we can use a normal distribution to approximate a binomial distribution We will want to do this when the number of trials of the binomial distribution gets larger Suppose we are given a binomial distribution associated with a binomial experiment involving n independent trials each with a probability of success p and a probability of failure q Then if n is large and p is not close to 0 or 1 the binomial distribution can be approximated by a normal distribution with u np and a 1 n q Using this mean and standard deviation these problems work just like the last few except for ONE LITTLE TWIST When we are approximating the binomial distribution by the normal distribution we are actually estimating the area of the rectangles in the histogram by the area under a normal curve But for X 5 PX 5 is represented by a rectangle that runs from 45 to 55 with height PX 5 So the area for less than five successes actually starts at 45 not 5 Here are two examples In the first n 15 and in the second n 6 1 quot all I lf39lj39l Norma PDF 03 CthomiaIPDF I 2 125 015 302 51015 in 5 01 v05 a i D l 2 3 4 5 6 39 S 3113112121415 39 k My particular technique for keeping this straight I Start with the binomial random variable X and write the probability in question in the form PX 2 a or PX lt b or Pa lt X 5 b as determined by the question 2 Then create a normal random variable Y that gives the appropriate edges for the rectangles in the histogram we wish to add the areas of So for example if my question asks for P4 S X lt 9 Iwant to include the rectangle centered at 4 but not the one centered at 9 ie Iwant to estimate the areas of the rectangles at 4 5 6 7 and 8 My new normal variable becomes P35 lt Y lt 85 3 Then follow the procedure above to turn the normal variable into a standard normal variable so we can read the probability off the chart P35 ltYlt85P 33957 quotltzlt83957 039 039 4 Calculate the numbers above and use the looking up the probability on the standard normal distribution table techniques for the last section Example 3 A company claims that 35 of the households in a certain community use their Squeaky Clean cleanser In a neighborhood of 10 households what is the probability that between 40 and 45 households use the cleanser This is a binomial experiment Use the normal distribution to approximate the probability Example 4 Use the normal distribution to approximate the binomial distribution Suppose that a coin is weighted so that the probability of obtaining a head on a single toss is 03 If the coin is tossed 25 times what is the probability of getting a fewer than 10 heads b Between 9 and 12 heads inclusive 0 More than 8 heads

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