The Normal Distribution and the 68-95-99.7 Rule p.html p.html.

Slides:

Advertisements

Similar presentations

Introductory Statistics for Laboratorians dealing with High Throughput Data sets Centers for Disease Control.

Advertisements

STUDENTS WILL DEMONSTRATE UNDERSTANDING OF THE CALCULATION OF STANDARD DEVIATION AND CONSTRUCTION OF A BELL CURVE Standard Deviation & The Bell Curve.

Standard Normal Calculations 2.2 b cont. Target Goal: I can standardize individual values and compare them using a common scale Hw: pg 105: 13 – 15, pg.

Normal and Standard Normal Distributions June 29, 2004.

The Normal Distribution

Chapter 6: The Standard Deviation as a Ruler and the Normal Model

The Normal distributions BPS chapter 3 © 2006 W.H. Freeman and Company.

Chapter 6: Standard Scores and the Normal Curve

The Rule Normal Distributions.

Topic 3 The Normal Distribution. From Histogram to Density Curve 2 We used histogram in Topic 2 to describe the overall pattern (shape, center, and spread)

AP Statistics: Section 2.2 A. One particularly important class of density curves are Normal curves which describe Normal distributions. Normal curves.

NORMAL DISTRIBUTION Normal distribution- continuous distribution.

Chapter 6 Evan Johnson & Mike Bi, Period 1. Z-Scores ●The easiest way to compare two dissimilar values is to compare their standard deviations. ●Z-scores.

Did you know ACT and SAT Score are normally distributed?

Normal Distribution Z-scores put to use!

Chapter 11: Random Sampling and Sampling Distributions

Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 1 z-scores & t-scores (unit 2) Review –Normal Curve, Deviation Scores, Standard Deviation z-scores for scores.

Normal Distributions.

Section 2.2, Part 1 Standard Normal Calculations AP Statistics Berkley High School/CASA.

Describing Location in a Distribution. Measuring Position: Percentiles Here are the scores of 25 students in Mr. Pryor’s statistics class on their first.

Chapter 6 The Standard Deviation as a Ruler and the Normal Model.

A P STATISTICS LESSON 2 – 2 STANDARD NORMAL CALCULATIONS.

Stat 1510: Statistical Thinking and Concepts 1 Density Curves and Normal Distribution.

6.1B Standard deviation of discrete random variables continuous random variables AP Statistics.

And the Rule THE NORMAL DISTRIBUTION. SKEWED DISTRIBUTIONS & OUTLIERS.

NOTES The Normal Distribution. In earlier courses, you have explored data in the following ways: By plotting data (histogram, stemplot, bar graph, etc.)

Normal Curve 64, 95, 99.7.

Normal Distributions.

Math II UNIT QUESTION: Can real world data be modeled by algebraic functions? Standard: MM2D1, D2 Today’s Question: How is a normal distribution used to.

CHAPTER 3: The Normal Distributions

When we collect data from an experiment, it can be “distributed” (spread out) in different ways.

Take out homework and a pencil to prepare for the homework quiz! Check the file folder for your class to pick up graded work.

Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition.

An opinion poll asks, “Are you afraid to go outside at night within a mile of your home because of crime?” Suppose that the proportion of all adults who.

Ch 2 The Normal Distribution 2.1 Density Curves and the Normal Distribution 2.2 Standard Normal Calculations.

2.2 Standard Normal Calculations

+ Chapter 2: Modeling Distributions of Data Section 2.2 Normal Distributions The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.

Standard Normal Calculations 2.2 Standard Normal Calculations 2.2 Target Goal: I can standardize individual values and compare them using a common scale.

DO NOW1/29/14 Use the gas price data to answer the following questions. {$4.79, $4.60, $4.75, $4.66, $4.60} 1.Find the mean of the data (hint: average)

Normal Distributions (aka Bell Curves, Gaussians) Spring 2010.

Chapter 4 Lesson 4.4a Numerical Methods for Describing Data

3.5 Applying the Normal Distribution – Z Scores Example 1 Determine the number of standard deviations above or below the mean each piece of data is. (This.

Describing Distributions with Numbers BPS chapter 2 © 2010 W.H. Freeman and Company.

6.2 – USE NORMAL DISTRIBUTIONS Unit 6 – Data Analysis and Probability.

Chapter 131 Normal Distributions. Chapter 132 Thought Question 2 What does it mean if a person’s SAT score falls at the 20th percentile for all people.

Z-scores, normal distribution, and more.  The bell curve is a symmetric curve, with the center of the graph being the high point, and the two sides on.

The Normal Approximation for Data. History The normal curve was discovered by Abraham de Moivre around Around 1870, the Belgian mathematician Adolph.

CHAPTER 11 Mean and Standard Deviation. BOX AND WHISKER PLOTS  Worksheet on Interpreting and making a box and whisker plot in the calculator.

MATH 2311 Review for Exam 2.

Sampling Distributions

CHAPTER 6 Random Variables

NORMAL DISTRIBUTIONS MATH III LESSON 12 – 2.

Standard Deviation & Z-Scores

Describing Location in a Distribution

MATH Review for Exam 2.

Empirical Rule Rule Ch. 6 Day 3 AP Statistics

CHAPTER 3: The Normal Distributions

Warm Up If there are 2000 students total in the school, what percentage of the students are in each region?

Estimating with Confidence

Standard Normal Calculations 2.2 b cont.

PRACTICE A normal distribution of scores has a standard deviation of 10. Find the z-scores corresponding to each of the following values: a) A score of.

Measuring location: percentiles

Warm Up Your textbook provides the following data on the height of men and women. Mean Std. Dev Men Women ) What is the z score.

Normal Curve 10.3 Z-scores.

10-5 The normal distribution

Summary (Week 1) Categorical vs. Quantitative Variables

Combining Random Variables

Algebra 2 Normal Curve Analysis Practice

Warm-Up Algebra 2 Honors 3/25/19

Warm Up Your textbook provides the following data on the height of men and women. Mean Std. Dev Men Women ) What is the z score.

Presentation transcript:

The Normal Distribution and the Rule p.html p.html

Normal means typical  If the average woman is 5 feet 4 inches tall (64 inches) would you expect to see many women who are around that height?  Is it common to see women who are 6 feet tall?  Is it common to see women who are 4 feet tall?

Describing what is Normal  Mean (EVERY ONE KNOWS THIS ONE) This is the average, the center. Here it is 64. This is the average, the center. Here it is 64. It’s located right in the middle of the normal curve. It’s located right in the middle of the normal curve.

Describing what is Normal  Standard Deviation (NOT MANY KNOW THIS ONE) This tells us how spread out the distribution is. This tells us how spread out the distribution is. Here it is 3. Here it is 3.

What is a typical woman’s height?  68% of all women are within 1 standard deviation of the mean.  Here 68% of all women are within 3 inches of 64.

Going out farther…  95% of all women are within 2 standard deviations of the mean.  Here 95% of all women are within 6 inches of 64.

Almost all women are…  99.7% of all women are within 3 standard deviations of the mean.  Here 99.7% of all women are within 9 in. of 64.

 The average grade on the quiz was 30 points.  Could all of the kids gotten a 30?  Did half the kids get a 20 and the other half get a 40?  What would be a good score on the quiz?  What would be a bad score? This is not enough information. It leaves a lot of questions…

What if we were only given the standard deviation?  The standard deviation on the quiz was 5 points.  So we know the spread of the grades, but from where was the quiz centered?  How did the class do in general?  Was my grade good or bad? This would still leave us with plenty of questions…

With both Mean and St. Dev.  Consider the following statement:  The mean was 30 points and the standard deviation on the quiz was 5 points. Now we know that about 68% of the class scored between… Now we know that about 68% of the class scored between… 25 and 35 points 25 and 35 points Now we can say that it was rare to get a score that was above 40 points. Now we can say that it was rare to get a score that was above 40 points. It was extremely rare to score above 45 points. It was extremely rare to score above 45 points.

The Normal Distribution needs both statistics to survive.  We can also graph the quiz scores.

A typical score… was between 25 and 35 points

An extremely rare score…  What percent of the students did this student beat?

An extremely rare score…  About 99.7 percent scored between a 15 to 45. That does not include about 0.3%

An extremely rare score…  You would have to split this in half to get about 0.15%.  So out of 2000 students, only 3 would score that well!

Practice with Rule  Suppose the average height of boys at EHS is 66 inches, with a standard deviation of 4.5 inches.  Draw the normal curve representing this information.  Answer:

Practice with Rule  Suppose the average height of boys at EHS is 66 inches, with a standard deviation of 4.5 inches.  How tall is someone 2 standard deviations above the mean?  Answer: = 75 inches

Practice with Rule  Suppose the average height of boys at EHS is 66 inches, with a standard deviation of 4.5 inches.  What percent of boys are between 61.5 and 70.5 inches tall ?  Answer: 68%

Practice with Rule  Suppose the average height of boys at EHS is 66 inches, with a standard deviation of 4.5 inches.  How many SD’s above the mean is someone who is 79.5 inches tall?  Answer: 3

Practice with Rule  Suppose the average height of boys at Sweet Home is 66 inches, with a standard deviation of 4.5 inches.  What percent of boys are between 57 and 70.5 inches tall?  Answer: 68%+ the bit between 57 and %+13.5% = 81.5%