AP® Statistics 2006 Free-Response Questions Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. © 2006 The College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service, CollegeEd, connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. www.mymathscloud.com
2006 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) 4 (II) Probability PABPAPBPAB()()()()∪=+− ∩PABPABPB()()()=∩EXxxipi()==∑μVar( )Xxpixix== −∑s22μdiIf X has a binomial distribution with parameters n and p, then: PXknkpkpnk()()==−−FHGIKJ1μxnp=sxnpp=−()1μpp=s()pppn=−1If x is the mean of a random sample of size nfrom an infinite population with mean μ and standard deviation s, then: μμx=ssxn=www.mymathscloud.com
2006 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) 5 (III) Inferential Statistics Standardized test statistic:statisticparameterstandard deviation of statistic-Confidence interval: statistic critical valuestandard deviation of statistic±()()∑Single-Sample Statistic Standard Deviation of Statistic Sample Mean σnSample Proportion ppn()1−Two-Sample Statistic Standard Deviation of Statistic Difference of sample means σσ121222nn+Special case when σσ12=σ1112nn+Difference of sample proportions ppnppn11122211()( )−+−Special case when pp12=pp1−bg1112nn+Chi-square test statisticobservedexpectedexpected=−∑af2www.mymathscloud.com
2006 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. 6 STATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II grade — 75 Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. A large regional real estate company keeps records of home sales for each of its sales agents. Each month, the company publishes the sales volume for each agent. Monthly sales volume is defined as the total sales price of all homes sold by the agent during a month. The figure below displays the cumulative relative frequency plot of the most recent monthly sales volume (in hundreds of thousands of dollars) for these agents. (a) In the context of this question, explain what information is conveyed by the circled point. (b) What proportion of sales agents achieved monthly sales volumes between $700,000 and $800,000 ? (c) For values between 10 and 11 on the horizontal axis, the cumulative relative frequency plot is flat. In the context of this question, explain what this means. (d) A bonus is to be given to 20 percent of the sales agents. Those who achieved the highest monthly sales volume during the preceding month will receive a bonus. What is the minimum monthly sales volume an agent must have achieved to qualify for the bonus? www.mymathscloud.com
