[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-538034-105":59,"doc-detail-538034-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","samples-to-success-probability-mathematics-high-school-statistics-statistics-and-probability","Samples to Success - Probability - Mathematics High School Statistics & Statistics and Probability","","Samples to Success provides sample items to clarify how students engage with different texts, tasks, and classroom contexts, while supporting educators in understanding proficiency expectations. The statistics and probability sections include ACT-aligned item types that reinforce core skills such as describing distribution center and spread, applying data collection methods, analyzing relationships in bivariate data, and calculating probabilities using sample spaces. Included questions span performance levels to guide instruction and assessment.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/samples-to-success-probability-mathematics-high-school-statistics-statistics-and-probability/538034/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/samples-to-success-probability-mathematics-high-school-statistics-statistics-and-probability/538034.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-10",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What core skills do the statistics and probability sample questions target?","Question",{"text":112,"@type":113},"They require students to describe center and spread of distributions, apply and analyze data collection methods, model relationships in bivariate data, and calculate probabilities using sample spaces.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the probability items connected to ACT-style assessment?",{"text":117,"@type":113},"The included sample questions blend typical ACT item formats with classroom-suitable questions designed to reinforce and develop skills assessed on the ACT.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of probability scenarios appear in the questions?",{"text":121,"@type":113},"The scenarios include arrangements and selections (books, committees, digits), real-world displays, expected values from coin tosses, and choosing members under constraints like excluding officers.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},538034,1791796580,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Samples to Success  \nSample items provide valuable insight into how students engage with different texts, tasks, and contexts by highlighting the types of opportunities they need for success in the classroom. These items offer a shared reference point for understanding proficiency expectations, complementing the assessment's role in measuring learning. Analyzing items alongside performance data can enable educators can gain a deeper understanding of students' strengths and areas for growth. Students thrive in environments rich with diverse materials, challenges that vary in task type, and multiple avenues for demonstrating understanding. High-quality instruction, aligned with the learning goals, is the most effective way to support students' growth and prepare them for success.  \nPROBABILITY  \nThe sample questions included in this rubric are a blend of those typical of the ACT and others that are suitable for classroom instruction, aimed at reinforcing and developing the skills assessed on the ACT. The statistics and probability content require students to describe center and spread of distributions; apply and analyze data collection methods; understand and model relationships in bivariate data ; and calculate probabilities, includingthe related sample spaces. This document contains ACT items and includes excerpts from ACT alignment guides: © ACT Education Corp.  \nMATHEMATICS HIGH SCHOOL STATISTICS &  \nStatistics and Probability  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nIn how many different ways can 3 books be arranged on a shelf?  \nA. 3  \nB. 6  \nC. 9  \nD. 12  \nE. 27  \nIn how many different ways can a committee of 4 people be chosen from a group of 8?  \nA. 32  \nB. 70  \nC. 72  \nD. 84  \nE. 196  \nHow many different 4-digit numbers can be formed using the digits 0-9, if the digits cannot be repeated and the number cannot begin with a 0?  \nA. 720  \nB. 3024  \nC. 4536  \nD. 5040  \nE. 10,000  \nIn a window display at a flower shop, there are 3 spots for 1 plant each. To fill these 3 spots, Emily has 6 plants to select from, each a different type. Selecting from the 6 plants, Emily can make how many possible display arrangements with 1 plant in each spot? (Note: The position of the unselected plants does not matter. )  \nA. 3  \nB. 6  \nC. 15  \nD. 120  \nE. 216  \nStatistics and Probability  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nWhat is the difference between the mean and the median of the set {3, 8, 10, 15}?  \nA. 0  \nB. 1  \nC. 4  \nD. 9  \nE. 12  \nYvette has 6 pairs of leggings, 2 pairs of shoes, and 6 T-shirts, which all go together well. How many different groupings consisting of 1 of her 6 pairs of leggings, 1 of her 2 pairs of shoes, and 1 of her 6 T-shirts are available for Yvette to wear?  \nA. 8  \nB. 12  \nC. 14  \nD. 24  \nE. 72  \nFor a given set of data, the standard score, 􀝖, corresponding to the raw score,􀝔, is given by 􀝖 = 􀯫~~ ~~􀰓, where 􀟤 is the mean of the set and 􀟪 is the standard deviation. If, for a set of score, 􀟤 = 78 and 􀟪 = 6, which of the following is the raw score, 􀝔, corresponding to 􀝖 = 2?  \nA. 90  \nB. 84  \nC. 80  \nD. 76  \nE. 66  \nAt the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads face up. Let the random variable 􀝔 represent the total number of points awarded on any toss of the coins. What is the expected value of 􀝔?  \nA.  \nB.  \n1  \n3 2  \n9 C.  \n2  \nD. 6  \nE. 9  \nStatistics and Probability  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nThe 35-member History Club is meeting to choose a student government representative. The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Hiroko, who is a member of the club but NOT an officer, will be chosen?  \nA.  \nB.  \nC.  \nD.  \n0  \n 4   \n35  \n 1   \n35  \n1 3  \nE.  \n1  \n32  \nTo make","cbCaipx6AjrHWcY1","https://ap.wps.com/l/cbCaipx6AjrHWcY1","pdf",312694,"English","# PROBABILITY\n## Mathematics High School Statistics & Statistics and Probability\n## Statistics and Probability","[{\"question\":\"What core skills do the statistics and probability sample questions target?\",\"answer\":\"They require students to describe center and spread of distributions, apply and analyze data collection methods, model relationships in bivariate data, and calculate probabilities using sample spaces.\"},{\"question\":\"How are the probability items connected to ACT-style assessment?\",\"answer\":\"The included sample questions blend typical ACT item formats with classroom-suitable questions designed to reinforce and develop skills assessed on the ACT.\"},{\"question\":\"What kinds of probability scenarios appear in the questions?\",\"answer\":\"The scenarios include arrangements and selections (books, committees, digits), real-world displays, expected values from coin tosses, and choosing members under constraints like excluding officers.\"}]","Samples to Success - Probability - Mathematics High School Statistics & Statistics and Probability | PDF",1791606029]