## Probability and Statistics

### Enrollment Message:

Students must have access to YouTube. Students must also possess a graphing calculator or access to an online graphing calculator.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.
**Prerequisites:**Algebra 2

**Course Objectives:** 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 dot plot or stem plot
- 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

**Course Outline:**

Exploring Data

Collecting Data

Probability

Probability Distributions

Sampling Distributions

Inference

**Resources Included:** Online lesson instruction and activities, opportunities to engage with a certified, online instructor and classmates, when appropriate, and online assessments to measure student performance of course objectives and readiness for subsequent academic pursuits.

**Additional Costs:** Graphing calculator.

**Scoring System: **Michigan Virtual does not assign letter grades, grant credit for courses, nor issue transcripts or diplomas. A final score reported as a percentage of total points earned will be sent to students upon completion of a course. Your school mentor is also able to access this score within the Student Learning Portal. Schools may use this score for conversion to their own letter grading system.

**Time Commitment:** Semester sessions are 18-weeks long: Students must be able to spend 1 or more hours per day in the course to be successful. Summer sessions are 10 weeks long: Students must be able to spend a minimum of 2 or more hours per day, or about 90 hours during the summer, for the student to be successful in any course. Trimester sessions are 12-weeks long: Students must be able to spend 1.5 or more hours per day in the course to be successful.

**Technology Requirements: ** Students will require a computer device with headphones, a microphone, webcam, up-to-date Chrome Web Browser, and access to YouTube.

Please review the Michigan Virtual Technology Requirements: https://michiganvirtual.org/about/support/knowledge-base/technical-requirements/

Lightweight devices such as Apple iPads, Google Chromebooks, and tablets have limited support for Java which still appears in a small percentage of FLVS courses. FLVS has worked to de-Flash its courses. Students may need extra work-around steps or alternate browsers to engage with some portions of select courses or may be required to utlize text-alternatives for some interactive objects. FLVS recommends students have a Windows or Mac based computer available to complete coursework in the event that your selected mobile device does not meet the needs of the course. Fully supported Operating Systems for FLVS courses include Windows (7 or higher), Mac OS X (10.8 or higher), and MacOS (10.12 or higher). Supported Browsers include the most recent versions of Microsoft Edge, Mozilla Firefox, Google Chrome, and Apple Safari on devices that support Java and HTML5. Browsers need to be up to date, and some FLVS courses may require installation or enabling of the following Plug-ins: JavaScript enabled, Cookies enabled, Java installed. https://www.flvs.net/student-resources/system-requirements

**Instructor Support System: **For technical issues within your course, contact the Customer Care Center by email at [email protected] or by phone at (888) 889-2840.

**Instructor Contact Expectations: **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.

**Academic Support Available: **In addition to access to a highly qualified, Michigan certified teacher, students have access to academic videos and outside resources verified by Michigan Virtual. For technical issues within the course, students can contact the Michigan Virtual Customer Care by email at [email protected] or by phone at (888) 889-2840.

**Required Assessment: **Online assessments consist of formative and summative assessments represented by computer-graded multiple choice, instructor-graded writing assignments including hands-on projects, model building and other forms of authentic assessments.

**Technical Skills Needed:** Basic technology skills necessary to locate and share information and files as well as interact with others in a Learning Management System (LMS), include the ability to:

- Download, edit, save, convert, and upload files
- Download and install software
- Use a messaging service similar to email
- Communicate with others in online discussion or message boards, following basic rules of netiquette
- Open attachments shared in messages
- Create, save, and submit files in commonly used word processing program formats and as a PDF
- Edit file share settings in cloud-based applications, such as Google Docs, Sheets, or Slides
- Save a file as a .pdf
- Copy and paste and format text using your mouse, keyboard, or an html editor’s toolbar menu
- Insert images or links into a file or html editor
- Search for information within a document using Ctrl+F or Command+F keyboard shortcuts
- Work in multiple browser windows and tabs simultaneously
- Activate a microphone or webcam on your device, and record and upload or link audio and/or video files
- Use presentation and graphics programs
- Follow an online pacing guide or calendar of due dates
- Use spell-check, citation editors, and tools commonly provided in word processing tool menus
- Create and maintain usernames and passwords

**Additional Information:** None