Curriculum / Math / 11th Grade / Unit 8: Probability and Statistical Inference / Lesson 8
Math
Unit 8
11th Grade
Lesson 8 of 13
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Lesson Notes
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Derive and calculate population percentages based on a normal distribution of data.
The core standards covered in this lesson
S.IC.A.2 — Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
S.IC.B.4 — Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
The foundational standards covered in this lesson
S.ID.A.4 — Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
The mean of this distribution is approximately 8, and the standard deviation is approximately 2. The number across the top describes how many balls landed in each numbered bin. There were 5,498 balls that were put in the Plinko game.
What percent of the balls fall between one standard deviation less and one standard deviation more than the mean?
What percent of the balls fall between two standard deviations less and two standard deviations more than the mean?
PhET Interactive Simulations University of Colorado Boulder https://phet.colorado.edu
Below is a normal distribution that shows the height of 8-year-old boys in inches. The relative frequency of each height is shown along the $${y-}$$axis, and the height, in inches, is shown along the $${x-}$$axis.
The mean is 50 and the standard deviation is 2.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The histogram below shows the distribution of heights (to the nearest inch) of 1,000 young women.
Algebra II > Module 4 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Use $${z-}$$scores to identify population percentiles.
Topic A: Probability
Determine probabilities of mutually exclusive events.
Standards
S.CP.A.1
Determine probabilities of events that are not mutually exclusive.
S.CP.A.1S.CP.B.6S.CP.B.7
Calculate conditional probabilities.
S.CP.A.3
Determine when events are independent and describe independent events using everday language.
S.CP.A.2S.CP.A.3S.CP.A.5
Calculate relative frequencies in two-way tables to analyze data and determine independence.
S.CP.A.4
Use conditional probability to make decisions about medical testing.
S.CP.A.2S.CP.A.3
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Topic B: The Normal Distribution
Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.
S.IC.A.1
S.IC.A.2S.IC.B.4
S.IC.B.4
Topic C: Statistical Inferences and Conclusions
Describe and compare statistical study methods.
S.IC.B.3S.IC.B.6
Use multiple random samples to estimate a population mean or proportion and verify the validity of the sampling method by analyzing the means and standard errors of samples.
Calculate and describe the margin of error in context and use larger sample sizes to minimize the margin of error.
Compare two treatments in experimental data and determine if the difference between the two treatments is significant.
S.IC.B.5
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