MATH 2311-06 Section 4.2. The Normal Distribution A density curve that is symmetric, single peaked and bell shaped is called a normal distribution. The.

Slides:

Advertisements

Similar presentations

Based upon the Empirical Rule, we know the approximate percentage of data that falls between certain standard deviations on a normal distribution curve.

Advertisements

The Normal Distribution

Did you know ACT and SAT Score are normally distributed?

Normal Distribution Z-scores put to use!

Normal Distributions Review

Unit 5 Data Analysis.

Created by: Tonya Jagoe. Notice The mean is always pulled the farthest into the tail. The median is always in the middle – located between the mean and.

Density Curves and the Normal Distribution

Normal Distributions.

In 2009, the mean mathematics score was 21 with a standard deviation of 5.3 for the ACT mathematics section. ReferenceReference Draw the normal curve in.

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

Essential Statistics Chapter 31 The Normal Distributions.

Think about this…. If Jenny gets an 86% on her first statistics test, should she be satisfied or disappointed? Could the scores of the other students in.

AP Statistics Chapter 2 Notes. Measures of Relative Standing Percentiles The percent of data that lies at or below a particular value. e.g. standardized.

Chapter 7 Lesson 7.6 Random Variables and Probability Distributions 7.6: Normal Distributions.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 6 Probability Distributions Section 6.2 Probabilities for Bell-Shaped Distributions.

Standard Deviation and the Normally Distributed Data Set

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Section 2.1 Density Curves. Get out a coin and flip it 5 times. Count how many heads you get. Get out a coin and flip it 5 times. Count how many heads.

CONTINUOUS RANDOM VARIABLES

MATH 110 Sec 14-4 Lecture: The Normal Distribution The normal distribution describes many real-life data sets.

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

Has a single peak at the center. Unimodal. Mean, median and the mode are equal and located in the center of the curve. Symmetrical about the mean. Somewhat.

Section 2.4: Measures of Spread. Example: Using the number of days of vacation for 6 students, find the range, variance and standard deviation. (this.

Chapter 9 – The Normal Distribution Math 22 Introductory Statistics.

Chapter 7 The Normal Probability Distribution 7.1 Properties of the Normal Distribution.

Normal Probability Distributions. Intro to Normal Distributions & the STANDARD Normal Distribution.

Normal Distributions. Probability density function - the curved line The height of the curve --> density for a particular X Density = relative concentration.

Density Curves & Normal Distributions Textbook Section 2.2.

15.5 The Normal Distribution. A frequency polygon can be replaced by a smooth curve A data set that is normally distributed is called a normal curve.

Simulations and Normal Distribution Week 4. Simulations Probability Exploration Tool.

Normal Probability Distributions Normal Probability Plots.

Section 2.1 Density Curves

2.2 Normal Distributions

Homework Check.

The Normal Distribution

Describing Location in a Distribution

Lesson 15-5 The Normal Distribution

Statistics Objectives: The students will be able to … 1. Identify and define a Normal Curve by its mean and standard deviation. 2. Use the 68 – 95 – 99.7.

Using the Empirical Rule

Standard and non-standard

AP Statistics Empirical Rule.

CONTINUOUS RANDOM VARIABLES

Chapter 12 Statistics 2012 Pearson Education, Inc.

Theoretical Normal Curve

Density Curve A mathematical model for data, providing a way to describe an entire distribution with a single mathematical expression. An idealized description.

Section 2.2: Normal Distributions

Interpreting Center & Variability.

ANATOMY OF THE EMPIRICAL RULE

2.1 Normal Distributions AP Statistics.

NORMAL PROBABILITY DISTRIBUTIONS

Warmup What is the height? What proportion of data is more than 5?

12/1/2018 Normal Distributions

The Standard Normal Bell Curve

Interpreting Center & Variability.

Empirical Rule MM3D3.

Normal Distributions, Empirical Rule and Standard Normal Distribution

EQ: How do we approximate a distribution of data?

Chapter 6: Normal Distributions

10-5 The normal distribution

MATH 2311 Section 4.1.

MATH 2311 Section 4.2.

Chapter 3: Modeling Distributions of Data

Density Curves and the Normal Distributions

Normal Distributions and the Empirical Rule

WarmUp A-F: put at top of today’s assignment on p

Chapter 12 Statistics.

MATH 2311 Section 4.2.

MATH 2311 Section 4.1.

Presentation transcript:

MATH Section 4.2

The Normal Distribution A density curve that is symmetric, single peaked and bell shaped is called a normal distribution. The normal distribution with mean μ and standard deviation σ is represented by N(μ, σ).

The Empirical Rule: The Empirical Rule states if a distribution has a normal distribution, 1.Approximately 68% of all observations fall within one standard deviation of the mean. 2. Approximately 95% of all observations fall within two standard deviations of the mean. 3. Approximately 99.7% of all observations fall within three standard deviations of the mean.

The Empirical Rule:

Example: The length of time needed to complete a certain test is normally distributed with mean 60 minutes and standard deviation 10 minutes. What is the probability that someone will take between 40 and 80 minutes to complete the test? Sketch the distribution and shade in the area in question.

Example: The length of time needed to complete a certain test is normally distributed with mean 60 minutes and standard deviation 10 minutes. What is the probability that someone will take between 40 and 80 minutes to complete the test? Sketch the distribution and shade in the area in question.

Example: The length of time needed to complete a certain test is normally distributed with mean 60 minutes and standard deviation 10 minutes. What is the probability that someone will take between 40 and 80 minutes to complete the test? Sketch the distribution and shade in the area in question. Find the interval that contains the middle 68% of completion times for all people taking the test. What percent of people take more than 80 minutes to complete the test?

Other Probabilities: What if our values are not exactly within one, two or three standard deviations from the mean? Probabilities forthese can still be found a number of ways, one of which we will explore in the next section. Using R, the probability can be found with the command pnorm(X, μ, σ). Note that the command in R only gives the probability that X is less than a given value. If we need to find the probability that X is greater than the given value, we will need to subtract the answer from 1. With the TI-83 and TI-84 calculator, the command is normalcdf(lower_limit, upper_limit, μ, σ).

Popper 7: (Continued from above example) 1. What is the probability that someone will take less than 45 minutes to complete the test? a. pnorm(45,60,10)b. 1-pnorm(45,60,10) c. pnorm(0,45)d. pnorm(45) 2. What is the probability that someone will take more than 30 minutes to complete the test? a. pnorm(30,60,10)b. 1-pnorm(30,60,10) c. pnorm(30,inf)d. 1-pnorm(30) 3. How long would it take someone to finish the test if they are in the top 10% of the times? (Approximate Answers) a. 70 minb. 75 minc. 80 min d. 85 min