# Probability and Statistics

## Course Description:

Probability and Statistics will introduce students to exploring data, sampling and experimentation by planning and conducting studies, anticipating patterns using probability and simulation, and employing statistical inference to analyze data and draw conclusions.

## Course Details:

Course Title (District): Probability and Statistics
Course Title (NCES SCED) : Probability and Statistics
Course Provider : Michigan Virtual
Content Provided By : Florida Virtual School
Online Instructor Provided By : Michigan Virtual
Standards Addressed : CCSS, MMC, NCAA
Academic Terms : Accelerated, Semester, Trimester
NCES SCED Code :
 Subject Area : Mathematics Course Identifier : Probability and Statistics Course Level : (G) General or Regular Available Credit : 0.5 Sequence : 1 of 1

## How To Enroll:

Enrollment Website : https://slp.michiganvirtual.org/ [email protected] (888) 889-2840

Students and Parents: It is important to work closely with your local school counselor or registrar to follow the school's enrollment procedures. By clicking the "Start Registration Request" button below, you will be able to notify the school of your interest in registering for the online course. However, it is the responsibility of the district or school to review the registration request and approve or deny the request. Please make a note to follow up with your school after submitting a registration request.

Upon completion of this course, students will be able to…

• Define and identify key terms including statistics and variables
• Quantitatively describe center of a data set
• Discuss the impact of data changes on measures of center
• Calculate the spread for a data set.
• Interpret data displayed in a dotplot or stemplot
• Compare distributions of univariate data
• Interpret data that is displayed in a boxplot
• Explain the difference between a sample data set and a population data set
• Discuss different sampling methods, including SRS, stratified, clusters, systemic, and multi-stage, and note any cautions that should be taken with each method.
• Discuss a variety of data collection methods, including census, survey, observational study, and experiments
• Identify and explain the three basic principles of experimental design
• Discuss and identify treatments, control groups, experimental units, random assignments, and replication
• Explain how confounding occurs and use good experimental design to correct study designs where confounding has occurred
• Explain the difference between correlation and causation in experimental design
• Assess study results, and identify whether correlation or causation can be established
• Use the rules of probability to compute probabilities of compound events
• Write out the sample space of a random phenomenon and use it to answer probability questions
• Use the basic rules of probability to solve problems
• use the rules of probability to compute probabilities of compound events
• Describe the concept of independence
• Perform a simulation of a probability situation using a table of random numbers or technology.
• Determine the classification of probability distributions as discrete or continuous
• Identify the conditions that must be met for a variable to be a binomial random variable
• Identify the conditions that must be met for a variable to be a geometric random variable
• Calculate the probabilities for geometric random variables
• Describe percentiles and recognize their meaning in context
• Perform transformations on data to create linearity
• Describe the characteristics of the normal (density) curve
• Use a Standard Normal distribution Table to answer questions about probability
• Calculate the mean and standard deviation of the sampling distribution
• Apply the Central Limit Theorem to problems involving sums and averages of variables from arbitrary distributions
• Interpret a confidence interval and confidence level
• Identify the components of a classical hypothesis test, including the parameter of interest, the null and alternative hypotheses and the test statistic
• Perform hypothesis tests on means and proportions for one or two populations
• Conduct inference for the mean of a Normal distribution where the underlying variance is either known or unknown, including the construction of confidence intervals and one and two—sided hypothesis tests
• Explain statistical significance
• Describe and compare explanatory and response variables
• Interpret a LSRL
• Make predictions using a LSRL

INACOL Online Course Quality Standards

The goals and objectives clearly state what the participants will know or be able to do at the end of the course. The goals and objectives are measurable in multiple ways. Fully Met The goals and objectives are clearly stated in the syllabus. They are measured at least in the pretest, unit tests, and discussion based assessments.
The course content and assignments are aligned with the state’s content standards, Common Core curriculum, or other accepted content standards set for Advanced Placement® courses, technology, computer science, or other courses whose content is not included in the state standards. Fully Met The course appears to be well aligned with the Common Core State Standards for Probability and Statistics.
The course content and assignments are of sufficient rigor, depth and breadth to teach the standards being addressed. Fully Met Each lesson includes multiple opportunities for students to practice and master the content in various ways.
Information literacy and communication skills are incorporated and taught as an integral part of the curriculum. Fully Met
Multiple learning resources and materials to increase student success are available to students before the course begins. Fully Met Students are provided with the necessary learning resources in the Syllabus, Unit 0, and Getting Started section. Nothing is available to students before the course begins though.
Course Overview and Introduction Rating Comments
Clear, complete course overview and syllabus are included in the course. Fully Met The course overview is included in the syllabus, pacing guide, and Welcome section of the course.
Course requirements are consistent with course goals, are representative of the scope of the course and are clearly stated. Fully Met Course requirements are clearly stated in the syllabus.
Information is provided to students, parents and mentors on how to communicate with the online instructor and course provider. Fully Met Provided in the Michigan Virtual Blackboard learning management system (LMS).
Legal and Acceptable Use Policies Rating Comments
The course reflects multi-cultural education, and the content is accurate, current and free of bias or advertising. Fully Met
Expectations for academic integrity, use of copyrighted materials, plagiarism and netiquette (Internet etiquette) regarding lesson activities, discussions, and e-mail communications are clearly stated. Fully Met Provided in the Michigan Virtual Blackboard LMS.
Privacy policies are clearly stated. Fully Met Provided in the Michigan Virtual Blackboard LMS.
Online instructor resources and notes are included. Fully Met An eteacher guide is provided in the instructor only section.
Assessment and assignment answers and explanations are included. Fully Met This can be found in the Instructor Only section of the course.
Instructional and Audience Analysis Rating Comments
Course design reflects a clear understanding of all students’ needs and incorporates varied ways to learn and master the curriculum. Partially Met Most of the lesson content is presented in written format. Very little use of videos or alternative methods.
Course, Unit and Lesson Design Rating Comments
The course is organized by units and lessons that fall into a logical sequence. Each unit and lesson includes an overview describing objectives, activities, assignments, assessments, and resources to provide multiple learning opportunities for students to master the content. Fully Met Unit overviews can be found in the diagnostic test links. Lesson overviews can be found at the bottom of the first page of each lesson.
Instructional Strategies and Activities Rating Comments
The course instruction includes activities that engage students in active learning. Fully Met
The course and course instructor provide students with multiple learning paths, based on student needs that engage students in a variety of ways. Fully Met The course itself provides many interactive components and guided practice within the lessons. The instructor can add additional resources to Blackboard to support student learning.
The course provides opportunities for students to engage in higher-order thinking, critical reasoning activities and thinking in increasingly complex ways. Fully Met
The course provides options for the instructor to adapt learning activities to accommodate students’ needs. Fully Met The instructor cannot adapt the lessons, but can add content in Blackboard.
Readability levels, written language assignments and mathematical requirements are appropriate for the course content and grade-level expectations. Fully Met
The course design provides opportunities for appropriate instructor-student interaction, including opportunities for timely and frequent feedback about student progress. Fully Met The course includes DBAs which require instructor-student interaction and specific feedback. The instructor may also provide feedback on projects, quizzes, and tests throughout the course.
The course design includes explicit communication/activities (both before and during the first week of the course) that confirms whether students are engaged and are progressing through the course. The instructor will follow program guidelines to address non-responsive students. Fully Met Michigan Virtual instructor guidelines ensure such interaction through welcome letters, instructor introductions, and regular progress reporting.
The course provides opportunities for appropriate instructor-student and student-student interaction to foster mastery and application of the material. Partially Met There is little student-student interaction in this course other than the discussion board assignment in Unit 0. There is plentiful teacher-student interaction.
Students have access to resources that enrich the course content. Fully Met Multiple types of resources are located within the lessons. I was not able to locate additional resources in Blackboard, but they are in the LTI.
Student evaluation strategies are consistent with course goals and objectives, are representative of the scope of the course and are clearly stated. Fully Met
The course structure includes adequate and appropriate methods and procedures to assess students’ mastery of content. Fully Met
Ongoing, varied, and frequent assessments are conducted throughout the course to inform instruction. Fully Met
Assessment strategies and tools make the student continuously aware of his/her progress in class and mastery of the content. Fully Met
Assessment Resources and Materials Rating Comments
Assessment materials provide the instructor with the flexibility to assess students in a variety of ways. Fully Met Assessment is provided through projects, quizzes, tests, and DBAs.
Grading rubrics are provided to the instructor and may be shared with students. Partially Met Rubrics are provided for projects and DBAs for the teacher only.
The grading policy and practices are easy to understand. Fully Met
The course architecture permits the online instructor to add content, activities and assessments to extend learning opportunities. Partially Met Instructors cannot alter content provided by the course vendor, but Michigan Virtual instructors are permitted to add supplemental materials as needed via the Blackboard LMS.
The course accommodates multiple school calendars; e.g., block, 4X4 and traditional schedules. Fully Met The calendar within the learning management system permits adjustments to the pacing guides, though Michigan Virtual has established start and end dates for fall, spring, summer, and trimester enrollment terms.
Clear and consistent navigation is present throughout the course. Partially Met Some lessons open within the Bb window and the breadcrumbs can be used to return to the unit menu. Other lessons open in a new window and need to be closed to return to the unit menu.
Rich media are provided in multiple formats for ease of use and access in order to address diverse student needs. Partially Met Most lesson activities are presented in written formats and are able to be printed.
Technology Requirements and Interoperability Rating Comments
All technology requirements (including hardware, browser, software, etc...) are specified. Fully Met Communicated in the syllabus, the Michigan Virtual website, and the Blackboard LMS.
Prerequisite skills in the use of technology are identified. Fully Met Prerequisite tech skills are listed in the syllabus.
The course uses content-specific tools and software appropriately. Fully Met
The course is designed to meet internationally recognized interoperability standards. Fully Met
Copyright and licensing status, including permission to share where applicable, is clearly stated and easily found. Fully Met Communicated within the Michigan Virtual Acceptable Use Policy (AUP) through the website and the LMS.
Course materials and activities are designed to provide appropriate access to all students. The course, developed with universal design principles in mind, conforms to the U.S. Section 504 and Section 508 provisions for electronic and information technology as well as the W3C’s Web Content Accessibility guidelines (WCAg 2.0). Partially Met This rating is based upon limited testing of select WCAG 2.0 principles and guidelines. Further testing may be necessary to ensure full compliance.
Student information remains confidential, as required by the Family Educational Rights and Privacy Act (FERPA). Fully Met Course is password protected; the privacy policy is communicated in the Blackboard LMS.
The course provider uses multiple ways of assessing course effectiveness. Fully Met Students have the ability to rate the lesson as completed and provide an evaluation of the course experience and support in an end-of-course survey. Michigan Virtual also has access to additional data regarding student success and satisfaction with courses.
The course is evaluated using a continuous improvement cycle for effectiveness and the findings used as a basis for improvement. Fully Met Michigan Virtual and FLVS update courses on a regular cycle.
The course is updated periodically to ensure that the content is current. Fully Met Michigan Virtual and FLVS update courses on a regular cycle.
Course instructors, whether faceto-face or virtual, are certificated and “highly qualified.” The online course teacher possesses a teaching credential from a state-licensing agency and is “highly qualified” as defined under ESEA. Fully Met All Michigan Virtual instructors are certified in the state of Michigan, endorsed within their assigned content areas and grade levels, and highly qualified under state and federal guidelines.
Instructor and Student Support Rating Comments
Professional development about the online course delivery system is offered by the provider to assure effective use of the courseware and various instructional media available. Fully Met Michigan Virtual instructors complete an onboarding course prior to teaching, annual professional development and conference attendance, participate in monthly department meetings, and are provided online resources for various instructional media.
The course provider offers technical support and course management assistance to students, the course instructor, and the school coordinator. Fully Met Michigan Virtual instructors have access to the Michigan Virtual Knowledge Base with tutorials to assist them as well as a technical support ticketing system to request additional support for technical issues in a course. Students also have a Customer Care center that offers technical support and course management assistance.
Course instructors, whether face-to-face or virtual, have been provided professional development in the behavioral, social, and when necessary, emotional, aspects of the learning environment. Fully Met
Course instructors, whether face-to-face or virtual, receive instructor professional development, which includes the support and use of a variety of communication modes to stimulate student engagement online. Fully Met
The provider assures that course instructors, whether face-to-face or virtual, are provided support, as needed, to ensure their effectiveness and success in meeting the needs of online students. Fully Met
Students are offered an orientation for taking an online course before starting the coursework. Fully Met Students are offered Michigan Virtual-specific orientation lessons and activites within all courses in addition to the Online Learning Orientation Tool (OLOT) located on the LMS homepage for students with no prior experience in taking an online course.

Review Conducted By : Michigan Virtual
Date of Review : 08/21/2019

Exploring Data
Collecting Data
Probability
Probability Distributions
Sampling Distributions
Inference

Term Type Enrollment Opens Enrollment Ends Random Draw Date Enrollment Drop Date Course Starts Course Ends # of Seats Course Fee Potential Additional Costs
Trimester 04/01/2020 01/04/2021 06/01/2020 10/23/2020 04/02/2021 100 \$325.0000 0.0000
Trimester 04/01/2020 04/12/2021 06/01/2020 01/08/2021 06/18/2021 100 \$325.0000 0.0000
Drop Policy Completion Policy Term Type Enrollment Opens Enrollment Ends
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Trimester 04/01/2020 01/04/2021
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Trimester 04/01/2020 04/12/2021

Students can use email or the private message system within the Student Learning Portal to access highly qualified teachers when they need instructor assistance. Students will also receive feedback on their work inside the learning management system. The Instructor Info area of their course may describe additional communication options

School Year Enrollment Count Pass Count Completion Rate Notes
19-20 151 115 76.2%