ࡱ>  ~ 7Qbjbj h{{IH$###Ps'#lHt(/// JTpGGGGGGG$ILH  H//&H"""//G"G""nGC?F/PqDۘ#VOD G,"$HH ! lHM : Prerequisite Review Sheet for MATH 1342, Elementary Statistics Most college-level math courses use some, but not absolutely all, of the skills students have developed in the earlier math classes. The point of this review is to illustrate the types of important prerequisite skills which are the most challenging for students in this course. Topics: Reading technical material: In reading technical material, often changes in just one word or even the order of the words, can make a difference in the meaning. Students must learn when and how to read carefully in this manner. Percentages Geometry and areas Plugging in numbers into formulas Rounding, exponents, mathematical notation. Solving equations: linear and proportional equations Formula for a straight line: Interpreting the coefficients, using the formula, graphing. How should I work the problems and grade them? Work through the problem list, checking your results in the brief answer key, and, if you cant see how to work it from there, look in the answer key with commentary for more help. Evaluate your understanding of each of the 27 problems by choosing one of these four descriptions. Keep track of your work in the grid below by checking one square for each problem. I worked it correctly, before I looked at the brief answer. I did not work it correctly at first, but as soon as I looked at the brief answer, I saw what I misunderstood and was able to correct it. I did not work it correctly at first, and the brief answer didnt help me enough, but after I read the answer with comments, I saw what I misunderstood and was able to correct it. I wasnt able to understand how to work the problem even after reading the answer with comments. 12345678910111213141516171819202122232425262728abcd The following patterns of answers indicate that you will probably need extra help from a knowledgeable person / tutor. (d) answers. 1 or 2 problems (c) or (d) answers: between 5 and 7 problems (b), (c), or (d) answers: between 7 and 10 problems Remember that the answers to the homework questions provided during the course will not have comments like the ones provided for these answers. Arrange now to get knowledgeable help outside of class at least twice a week, every week, so that you dont get behind. Students who are struggling, and who fall behind, are seldom able to complete the course. Missing more problems than indicated above is an indication that you are not yet ready for MATH 1342. Problems: 1. Giselle and Ruth are discussing when they will wear raincoats. Giselle says that she will wear a raincoat to school only if the weather report predicted more than a 50% chance of rain and, when she leaves in the morning, the sky is overcast. Ruth says that she will wear a raincoat to school if either the weather report predicted more than a 50% chance of rain or if, when she leaves in the morning, the sky is overcast. On Tuesday the weather report predicted a 40% chance of rain, but when the girls left for school, the sky was sunny. On Wednesday the weather report predicted a 40% chance of rain, and when the girls left for school, the sky was overcast. On Thursday, the weather report predicted a 60% chance of rain, and when the girls left for school, the sky was overcast. On Friday, the weather report predicted a 60% chance of rain, and when the girls left for school, the sky was sunny. Assuming that both girls acted as they claimed they would act, What days did Giselle wear a raincoat? What days did Ruth wear a raincoat? 2. Brent pays $550 per month for rent and his monthly salary is $1876. What proportion of his monthly salary is his rent? (This answer will be between 0.000 and 1.000) What percentage of his monthly salary is his rent? (This answer will be between 0.0% and 100.0%) 3. At Joliet High School, there are 325 seniors who entered Joliet schools in the fifth grade or lower, and 897 seniors who entered Joliet schools in the sixth grade or higher. What percentage of the seniors entered Joliet schools in the fifth grade or lower? 4. In a particular business college, the following table gives the numbers of men and women in various majors. What percentage of the women are accounting majors? MenWomentotalAccounting8369152Administration102110212Finance533790total238216454 5. The figure at the right has total area of 5.3 square feet. The shaded area is 2.9 square feet. What is the area of the unshaded part, labeled L?   6. A figure is divided into three non-equal pieces by lines. The three pictures at the top of the next page are all of the same figure with the same division lines. Different areas are shaded and labeled on each. Find the areas of the portions labeled B and C.  7. Round 17.39283 to the nearest thousandth. 8. Round 0.02397 to the nearest hundredth. 9. Use your calculator to find  EMBED Equation.DSMT4 , correct to 3 decimal places. 10. Use your calculator to find  EMBED Equation.DSMT4  11. When a scientific calculator shows the answer for a computation is 7.23E-04, what number does that represent? 12. Consider the mathematical statement:  EMBED Equation.DSMT4  How would you read that statement in words? Give four numbers that make that statement true. Give either a number line or an interval that indicates all the numbers that make that statement true. 13. Consider the mathematical statement:  EMBED Equation.DSMT4  How would you read that statement in words? Give four numbers that make that statement true. Give either a number line or an interval that indicates all the numbers that make that statement true. 14. Solve for x:  EMBED Equation.DSMT4  15. Solve for y:  EMBED Equation.DSMT4  16. Solve for r:  EMBED Equation.DSMT4  17. Solve for m :  EMBED Equation.DSMT4  18. Solve for k:  EMBED Equation.DSMT4  One way of writing the equation of a straight line is in the slope-intercept form:  EMBED Equation.DSMT4 , where m is the slope and b is the y-intercept. When we graph the equation of a line on a Cartesian coordinate system, usually we put y on the vertical axis and x on the horizontal axis. 19. For this equation of a line, identify the slope and the y-intercept.  EMBED Equation.DSMT4  20. For this equation of a line, identify the slope and the y-intercept.  EMBED Equation.DSMT4  21. For this equation of a line, identify the slope and the y-intercept.  EMBED Equation.DSMT4  22. For this equation of a line, identify the slope and the y-intercept.  EMBED Equation.DSMT4  23. Graph this line between  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  In the statistics course, the work is more about reasoning than about computation. Moreover, youll use software for much of the computation. Nevertheless, to be successful, you must be able to correctly evaluate formulas using a scientific calculator. When practicing evaluating new formulas with your calculator, it is a good idea to first use some easy numbers and do the problem in your head to make sure your calculator is giving you the right answer. This is the way to explore what order you need to enter the numbers. Only after you are completely clear about the order in which to enter the numbers should you start using it to calculate with numbers that are so messy you couldnt do it in your head. In each of the problems below, be sure you can do the first part easily before you attempt the second part. The answers are provided right here rather than in the answer key, but some commentary is given in the full answer key. Read it if youre having difficulties. 24.  EMBED Equation.DSMT4  a. Find L when  EMBED Equation.DSMT4  b. Find L when  EMBED Equation.DSMT4  c. Find L when  EMBED Equation.DSMT4  25.  EMBED Equation.DSMT4  a. Find w when  EMBED Equation.DSMT4  b. Find w when  EMBED Equation.DSMT4  26.  EMBED Equation.DSMT4  a. Find M when  EMBED Equation.DSMT4  b. Find M when  EMBED Equation.DSMT4  27.  EMBED Equation.DSMT4  a. Find R when  EMBED Equation.DSMT4  b. Find R when  EMBED Equation.DSMT4  28.  EMBED Equation.DSMT4  Find m when  EMBED Equation.DSMT4 . Find m when  EMBED Equation.DSMT4 . Brief answer key: Giselle wore a raincoat only on Thursday. Ruth wore a raincoat on Wednesday, Thursday, and Friday. a. 0.29318 b. 29.318% 26.596% 31.94% 2.4 sq. ft. B: 0.48; C: 0.31 17.393. 0.02 4.359 324 0.000723 x is less than 3.24. Many numbers make this true. Some numbers which make this true are 3.2, 1.8, and 0 and -9.3. In interval notation, this is  EMBED Equation.DSMT4  y is greater than or equal to 5.8. Many numbers make this true. Some numbers which make this true are 5.8, 6, 8.1, and 111.832. In interval notation, this is  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  m = 8.769 k = 263.3092 slope 4, y-intercept 7 slope 18, y-intercept 9.87. slope 6, y-intercept 3 . slope 0.000452, y-intercept 0.00723.  24. a. 17 b. -13 c. 14.281 25. a. 1.5 b. -0.6545 26. a. 6 b. 0.47548 27. a. 5 b. 1.66147 28. a. 10 b. 8.8408 Answer key with comments: (Skill: Reading Comprehension) Giselle wore a raincoat only on Thursday. Ruth wore a raincoat on Wednesday, Thursday, and Friday. This problem requires that you understand the difference in meaning between and and or and that you know to look for which of those words is used in each description. (Skill: Calculation proportions and percentages) a. 550/1876 = 0.29318 b. 0.29318 = 29.318% You must know the difference between proportion and percent and how to easily convert between them. (Skill: Setting up ratios and calculating percentages) 325/(325+897) = 0.26596 = 26.596% Notice that, to find the total number of seniors, you must add the two numbers given. Sometimes students assume that the two numbers given in the problem are the appropriate numbers to plug into a formula, and that is often not the case. (Skill: Setting up ratios and calculating percentages) 69/216 = 0.3194 = 31.94% The crucial point here is that you must be able to understand, by reading, the difference between the two questions What percentage of the women major in accounting? and What percent of the accounting majors are women? The difference in these two questions tells us the difference in the denominators we need to compute the answers. For the first question, the denominator is the total number of women. For the second question, the denominator is the total number of accounting majors. The question asked in the problem is What percentage of the women major in accounting? for which the answer is approximately 32% as shown in the first line of this solution. If this question were asked What percentage of the accounting majors are women? the answer would be 69/152 = 45.39%. (Skill: Logical reasoning with geometry) 2.4 sq. ft. Area of the un-shaded part is 5.3 2.9 = 2.4 (Skill: Logical reasoning with geometry) B: 0.48; C: 0.31. Area of B = 0.69 0.21 = 0.48. Area of C = 1.00 0.69 = 0.31 (Skill: Place value and rounding) 17.393. When you round, if the part you are leaving off is half or more, the previous digit is increased by 1. (Skill: Place value and rounding) 0.02. Notice that the part you are leaving off is less than half. (Skill: Understanding and calculating the square root of a number) 4.359 (Skill: Understanding and calculating the square of a number) 324. Notice the difference between taking the square root of a number and squaring a number. It is very important to be clear about which one youre doing. (Skill: Numbers in Scientific Notation and reading calculator output) 0.000723. This number is in scientific notation. It means  EMBED Equation.DSMT4  (Skill: Understanding and translating math inequality notation) x is less than 3.24. Many numbers make this true. Some numbers which make this true are 3.2, 1.8, and 0 and -9.3. In interval notation, this is  EMBED Equation.DSMT4  (Skill: Understanding and translating math inequality notation) y is greater than or equal to 5.8. Many numbers make this true. Some numbers which make this true are 5.8, 6, 8.1, and 111.832. In interval notation, this is  EMBED Equation.DSMT4  (Skill: Solving linear equations)  EMBED Equation.DSMT4 . It is also acceptable to write this answer as a mixed number,  EMBED Equation.DSMT4 , or as a decimal, y = 4.333. When you write answers in decimal form, often the accurate answer has an infinite decimal expansion. You do not have to list as many decimal places as your calculator gives you. Your instructor will give you more specific guidelines for various types of problems. When no guidelines are given and it seems reasonable, you should keep about three decimal places. (Skill: Solving linear equations)  EMBED Equation.DSMT4 . Again, it is acceptable to write this as an improper fraction as is given here, or as an equivalent mixed number,  EMBED Equation.DSMT4 , or as an equivalent decimal, y = 1.684 (Skill: Solving proportion equations)  EMBED Equation.DSMT4 . Again, it is acceptable to write this as an improper fraction, as given here, or an equivalent mixed number or an equivalent decimal number. (Skill: Solving proportion equations) m = 8.769 . In this problem, you must recognize how to solve a proportion equation when one of the sides is not written as a fraction. An easy way is to first turn it into a fraction, as  EMBED Equation.DSMT4  and then follow the same steps as in the previous problem. As part of the solution, you found  EMBED Equation.DSMT4  but that is not an acceptable final answer because fractions in final answers must have whole numbers for both the numerator and denominator. So you must divide these for an acceptable final answer. (Skill: Solving proportion equations involving a square root) k = 263.3092. Do this problem in a similar manner to the previous problem, except that, after you find  EMBED Equation.DSMT4 , square both sides. (Skill: Interpreting linear equations) slope 4, y-intercept 7 (Skill: Interpreting linear equations) slope 18, y-intercept 9.87. To write this in the form  EMBED Equation.DSMT4 , we have  EMBED Equation.DSMT4 , so the subtraction turns into a negative number for the y-intercept. (Skill: Interpreting linear equations) slope 6, y-intercept 3 . To write this in the form EMBED Equation.DSMT4 , we have to reverse the order of the two terms. In fact, we wouldnt rewrite it. Instead we make a point to think of the slope coefficient as the number that is multiplied by the x. It doesnt matter whether that term comes first or second. (Skill: Interpreting linear equations) slope 0.000452, y-intercept 0.00723. Notice that, if we had computed these coefficients, we should not be content to round all numbers to three decimal places, since wed lose too much information. If we have very small numbers, like these, we usually keep at least three decimal places past all leading zeros. (Skill: Graphing linear equations over a specific interval) You can choose any x-values in the appropriate interval to plug in. No matter what you choose, you should get the same line on a graph. x y 4 1.63 5 0.98 10 -2.27 30 -15.27 (Skill: Using formulas, order of operations) a. 17 b. -13 c. 14.281 There are different ways to enter these numbers and operations and obtain a correct answer, depending on the type of calculator, whether you use parentheses or not, and whether you use negative numbers or just change to subtractions, as appropriate. It is crucial that you understand, from previous math courses, the appropriate order of operations, that is, that the multiplication here must be done before the addition. Maybe your calculator handles that and maybe it doesnt, depending on how you enter the numbers. Be alert and think about the results. (Skill: Using formulas, order of operations) a. 1.5 b. -0.6545 Although it is best to be able to enter all the numbers in the calculator and have it compute one final result, sometimes that is difficult. Here youll need some parentheses in order to do that. If you cant make that work, then do some parts of it separately, write down the results, and then use your calculator with your written results to find the final answer. (I recommend about five decimal places for intermediate results, in order to have a reasonable chance of getting final results accurate to about three decimal places.) (Skill: Using formulas, order of operations) a. 6 b. 0.47548 Most students will want to do the three parts of this separately, write the results of each, and then add them together with a calculator at the end. (Skill: Using formulas, order of operations) a. 5 b. 1.66147 Notice that it is NOT CORRECT to take the square root of each part separately and add those. The formula says that you must add first and then take the square root. Sometimes we can change the order of operations because the two different ways are algebraically equivalent. But not here. (Skill: Using formulas, solving proportion equations) a. 10 b. 8.8408 Here, you will need to solve a proportion equation to obtain the answer. For part a, we have  EMBED Equation.DSMT4  becomes  EMBED Equation.DSMT4  Alternatively, you could just solve the equation first for m in terms of the other variables, and then plug in the values of the other variables.  EMBED Equation.DSMT4  Then, we have  EMBED Equation.DSMT4  It is acceptable for students in this course to always work these problems the first way illustrated here (plugging in numbers first and then solving) rather than the second way, which is more abstract.     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T  UU@@  LArrange now to get knowledgeableA).-)..B.-)-..B)--)).)TTUU@@LP TdVUU@@LThelp.(.TTWlUU@@WLP  T #rUU@@]Lloutside of class..#.)-()#$TT$ :rUU@@$]LP T,; rUU@@;]PLat least twice a week, every week, so that you don t get behind. Students who ())#A)))B()-)-)-B))-$..)-....--)-)...3..)-$B.. T t UU@@NLare struggling, and who fall behind, are seldom able to complete the course. ))#.--.-)..B..(.).-.()#)..F).(.).F.)).)(..$)TT tUU@@ LP ) TTDUU@@/LP ) TTGUU@@LP ,TGUU@@ LdMissing moreR#$.-F.)TTG+UU@@LP T,GUU@@,JLproblems than indicated above is an indication that you are not yet ready ..-)F$.(..-)().)..-)$)...))...(-..))..-))).- TbUU@@Lhfor MATH 1342..RB9B....TTcUU@@cLP )% % ( 666666666666666666666666666666666666 6 66 6  6 66 6  6 66 6  6 66 6  6 66 6 66666666666666666666  d."System???????????????--@Times New Roman--- p2 ,ZCdMATH 1342 Prerequisite Review Sheet 2 ,2 d 2 ,Kd 2 ,Xdupdated 2 ,wd5/23/15 2 ,d 3(2 ,d s2 ,d 2 ,dpage  2 ,d1 2 ,d 2 ,dof e 2 ,d1 2 ,d ,d'2 6dPlease sX2 63dend comments or corrections to mparker@austincc.edu  2 6d ,d'@Times New Roman---h2 R>dPrerequisite Review Sheet for MATH 1342, Elementary Statistics    2 Rd  2 _Zd @Times New Roman---2 kl dMost college  2 kd-C2 k%dlevel math courses use some, but not 2 kM dabsolutely (2 k}dall, of the skills s 2 kdstudents have F2 xZ'ddeveloped in the earlier math classes.   2 xd ^2 x7dThe point of this review is to illustrate the types of 2 Zdimpa2 kWdortant prerequisite skills which are the most challenging for students in this course.   2 d  2 ld ---2 ZdTopics---2 yd:  2 d @Symbol--- 2 ld@"Arial--- 2 qd ---2 ~ZdReading technical material: In reading technical material, often changes in just one word ,d'q2 ~Ddor even the order of the words, can make a difference in the meaning%2 d. Students must ,d'\2 ~6dlearn when and how to read carefully in this manner.   2 ld ,d'--- 2 ld--- 2 qd ---2 ~ dPercentages 2 d ,d'--- 2 ld--- 2 qd ---&2 ~dGeometry and areas  2 d ,d'--- 2 ld--- 2 qd ---=2 ~!dPlugging in numbers into formulass 2 d ,d'--- 2 ld--- 2 qd ---L2 ~+dRounding, exponents, mathematical notation. 2 Fd ,d'--- 2 ld--- 2 qd ---[2 ~5dSolving equations: linear and proportional equations  2 gd ,d'--- 2 ld--- 2 qd ---+2 ~dFormula for a straigh v2 Gdt line: Interpreting the coefficients, using the formula, graphing.   2 d ,d' 2 "Zd ---P2 /Z.dHow should I work the problems and grade them?    2 /Fd --- 2 ;Zd  2 HZd $2 H~ZdWork through the problem list, checking your results in the brief answer key, and, if you M2 UZ,dcant see how to work it from there, look in  2 Ud R2 U/dthe answer key with commentary for more help.   >2 aZ"dEvaluate your understanding of eac+2 adh of the 27 problems 82 aSdby choosing one of these four 2 nZ ddescriptions2 nd. Keeps 2 nd 82 ndtrack of your work in the grid 2 n4d D2 n6&dbelow by checking one square for each 2 zZdproblems 2 zd. 2 zd ---2 lda.--- 2 td ---2 ~ dI worked it 2 d 2 dcorrects2 dly2 d, be2 dfore c2 dI looked 2 !d )2 #dat the brief answer. 2 xd ,d'---2 ldb.--- 2 td ---A2 ~$dI did not work it correctly at firstU2 1d, but as soon as I looked at the brief answer, I i2  dsaw what I ,d'G2 ~(dmisunderstood and was able to correct it2 0d. o 2 8d ,d'---2 ldc.--- 2 td ---A2 ~$dI did not work it correctly at firstO2 -d, and the brief answer didnt help me enough, 2 d 2 dbut ak2 dfter I d,d'72 ~dread the answer with comments^2  7d, I saw what I misunderstood and was able to correct it  2 d. 2 d ,d'---2 ldd.--- 2 td ---b2 ~:dI wasnt able to understand how to work the problem even a 72 dfter reading the answer with ,d'2 ~dcomments  2 d. 2 d ,d' 2 Zd ,eU@Times New Roman--- 2 ZUe ',se---  2 jes1 2 nes ',t---  2 yt2 2 }t ',---  2 3 2  ',---  2 4 2  ',---  2 5 2  ',---  2 6 2  ',---  2 7 2  ',---  2 8 2  ',---  2 9 2  ',--- 2 10 2  ',--- 2 11 2   ',"--- 2 "12 2 " ',5#--- 2 (#513 2 0#5 ',H5--- 2 :5H14 2 C5H ',[H--- 2 MH[15 2 UH[ ',m[--- 2 `[m16 2 h[m ',n--- 2 sn17 2 {n ',--- 2 18 2  ',--- 2 19 2  ',--- 2 20 2  ',--- 2 21 2  ',--- 2 22 2  ',---  2 2 2 3 2  ',--- 2 24 2  ',--- 2  25 2  ',)--- 2 )26 2 $) ',<*--- 2 /*<27 2 7*< ',O=--- 2 B<O28 2 J<O '- @ !T-- @ !T-- @ !U-- @ !e-- @ !e-- @ !s-- @ !t-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !"-- @ !#-- @ !5-- @ !5-- @ !H-- @ !H-- @ ![-- @ ![-- @ !m-- @ !n-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !)-- @ !*-- @ !<-- @ !<-- @ !O-- @ !O-- @ ! 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