MA.912.DP.2.3

Estimate population percentages from data that has been fit to the normal distribution.

Clarifications

Clarification 1: Instruction includes using technology, empirical rules or tables to estimate areas under the normal curve.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessment

Area Under the Normal Curve:

Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.

Type: Formative Assessment

Lesson Plans

Texting and Standard Deviation:

This lesson uses texting to teach statistics. In the lesson, students will calculate the mean, median, and standard deviation. They will create a normal distribution using the mean and standard deviation and estimate population percentages. They will construct and interpret dot plots based on the data they collected. Students will also use similarities and differences in shape, center, and spread to determine who is better at texting, boys, or girls.

Type: Lesson Plan

Standard Deviation and the Normal Curve in Kahoot!:

In this three-day lesson, students learn about standard deviation, the normal curve, and how they are applied. Your students will be engaged and learning when they collect and analyze data using a free Kahoot! quiz.

Type: Lesson Plan

Picturing the Normal World:

This is an introductory lesson on normally distributed data. Students will calculate the standard deviation and use the Empirical Rule.

Type: Lesson Plan

How do we measure success?:

Students will use the normal distribution to estimate population percentages and calculate the values that fall within one, two, and three standard deviations of the mean. Students use statistics and a normal distribution to determine how well a participant performed in a math competition.

Type: Lesson Plan

If The Shoe Fits – A "Normal" Cinderella Story:

Using a normal distribution manipulative and a calculator, students will explore the normal distribution curve to determine the area between each standard deviation from the mean using the empirical rule. Students will use the mean and standard deviation to predict outcomes in real-world situations and finally answer the age old question: What size was Cinderella's glass slipper?

Type: Lesson Plan

The Cereal Prize Estimation:

How many boxes of cereal would you have to purchase to win all six prizes?

This lesson uses class data collected through simulations to allow students to answer this question. Students simulate purchasing cereal boxes and create a t-confidence interval with their data to determine how many boxes they can expect to buy.

Type: Lesson Plan

Sweet Statistics - A Candy Journey:

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

Type: Lesson Plan

Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

Florida State University Counseling Psychologist discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Sampling Strategies for Ecology Research in the Intertidal Zone:

Will Ryan describes methods for collecting multiple random samples of anemones in coastal marine environments.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Type: Problem-Solving Task

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Type: Problem-Solving Task

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Type: Problem-Solving Task

MFAS Formative Assessments

Area Under the Normal Curve:

Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Tasks

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Type: Problem-Solving Task

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Type: Problem-Solving Task

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Type: Problem-Solving Task

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Type: Problem-Solving Task

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Type: Problem-Solving Task