The Standard Normal Curve Revisited. Can you place where you are on a normal distribution at certain percentiles? 50 th percentile? Z = 0 84 th percentile?

Slides:

Advertisements

Similar presentations

Percentiles and the Normal Curve

Advertisements

Chapter – 5.4: The Normal Model

Calculations in the Bivariate Normal Distribution James H. Steiger.

The Normal Distribution

Normal distribution. An example from class HEIGHTS OF MOTHERS CLASS LIMITS(in.)FREQUENCY

Chapter 6: Standard Scores and the Normal Curve

Normal Distributions: Finding Values

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 6 Normal Probability Distributions

Normal Distributions.

In this chapter, we will look at using the standard deviation as a measuring stick and some properties of data sets that are normally distributed.

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.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 1 PROBABILITIES FOR CONTINUOUS RANDOM VARIABLES THE NORMAL DISTRIBUTION CHAPTER 8_B.

Section 2.5 The Normal Distribution.  68% of values lie within 1 SD of the mean.  Including to the right and left  90% of the values lie with

Warm-Up If the variance of a set of data is 12.4, what is the standard deviation? If the standard deviation of a set of data is 5.7, what is the variance?

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

1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Chapter 6. Continuous Random Variables Reminder: Continuous random variable.

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.

§ 5.4 Normal Distributions: Finding Values. Finding z-Scores Example : Find the z - score that corresponds to a cumulative area of z

Using the Calculator for Normal Distributions. Standard Normal Go to 2 nd Distribution Find #2 – Normalcdf Key stroke is Normalcdf(Begin, end) If standardized,

The Standard Normal Distribution

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.

 z – Score  Percentiles  Quartiles  A standardized value  A number of standard deviations a given value, x, is above or below the mean  z = (score.

Describing Location in a Distribution Chapter 2. 1.Explain what is meant by a standardized value. 2. Compute the z-score of an observation given the mean.

1 The Normal Distribution William P. Wattles Psychology 302.

MM2D1d:. Outlier—data that appears to deviate markedly from other members of the sample in which it occurs. For our purposes, any data that falls beyond.

Warm-Up On the driving range, Tiger Woods practices his golf swing with a particular club by hitting many, many balls. When Tiger hits his driver, the.

Normal Distribution and Z-scores

The Normal Distribution Section 8.2. The Galton Board Developed in the late 19 th century by Sir Francis Galton, a cousin of Charles Darwin Theorized.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 6 The Standard Deviation as a Ruler and the Normal Model.

SWBAT: Describe and Apply the Rule and the standard Normal Distribution. Do Now: Scott was one of 50 junior boys to take the PSAT at his school.

2.2 Standard Normal Calculations

Copyright ©2005 Brooks/Cole, a division of Thomson Learning, Inc. Bell-Shaped Curves and Other Shapes Chapter 8.

Chapter 5 Review. Find the area of the indicated region under the standard normal curve. Use the table and show your work. Find the areas to the left.

What does a population that is normally distributed look like? X 80  = 80 and  =

The Standard Normal Distribution Section Starter Weights of adult male Norwegian Elkhounds are N(42, 2) pounds. What weight would represent the.

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

Honors Advanced Algebra Presentation 1-6. Vocabulary.

In this chapter, we will look at using the standard deviation as a measuring stick and some properties of data sets that are normally distributed.

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.

Case Closed The New SAT Chapter 2 AP Stats at LSHS Mr. Molesky The New SAT Chapter 2 AP Stats at LSHS Mr. Molesky.

Chapter 3 Modeling Distributions of Data Page 101.

a) Here is a Normal curve for the distribution of batting averages. The mean and the points one, two and three standard deviations from the mean are labeled.

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.

Math 3Warm Up4/23/12 Find the probability mean and standard deviation for the following data. 2, 4, 5, 6, 5, 5, 5, 2, 2, 4, 4, 3, 3, 1, 2, 2, 3, 4, 6,

 The heights of 16-year-old males are normally distributed with mean 68 inches and a standard deviation 2 inches. Determine the z-score for: ◦ 70.

Bell Ringer 1.Mrs. Hall’s class had a test score average of 81.2%. The standard deviation was 5.8%. Assuming the scores had a normal distribution, what.

The Normal Distributions.  1. Always plot your data ◦ Usually a histogram or stemplot  2. Look for the overall pattern ◦ Shape, center, spread, deviations.

Normal Distribution and Z-scores

z-Scores, the Normal Curve, & Standard Error of the Mean

Normal Distribution.

Distributions and mathematical models

U6 - DAY 2 WARM UP! Given the times required for a group of students to complete the physical fitness obstacle course result in a normal curve, and that.

Other Normal Distributions

z-Scores, the Normal Curve, & Standard Error of the Mean

Applications of the Normal Distribution

2.2 Determining and Using Normal Distributions

What % of Seniors only apply to 3 or less colleges?

U6 - DAY 2 WARM UP! Given the times required for a group of students to complete the physical fitness obstacle course result in a normal curve, and that.

Warm Up – Tuesday The table to the left shows

Measuring location: percentiles

I can find any probability…from a normal distribution

Lecture 21 Section – Tue, Oct 10, 2006

Z-Scores The Normal Distribution

Applications of the Normal Distribution

Homework: pg. 136 #25, ) A. 2.5% B. Between 64 and 74 inches

The Normal Curve Section 7.1 & 7.2.

Normal Distribution with Graphing Calculator

Presentation transcript:

The Standard Normal Curve Revisited

Can you place where you are on a normal distribution at certain percentiles? 50 th percentile? Z = 0 84 th percentile? Z = percentile? Z = -2

Finding z-scores given the percentile Find the closest percentile on the table to get the z-score or… Use the invNorm command to find the z-score given the percentile or area under a normal curve. Press 2 nd, DIST, invNorm (percentile as a decimal #). For example, to find the z-score for the 75 th percentile, press invNorm (.75). For the standard normal distribution, What is the median (50%tile)? invNorm(.50) = 0 What is the lower quartile? invNorm(.25) = What z -score falls at the 95 th percentile? invNorm (.95) = What z-score has 30% of the data above it? invNorm(.70) =.524

SAT Example The approximately normal distribution of SAT scores for the 2009 incoming class at the University of Texas had a mean 1815 and a standard deviation 252. What did a student at University of Texas get on the SAT if his or her score was 1.6 standard deviations above the average? Z = = x – = x – 1815 X = or 2218 What score did a student get who is at the 90 th percentile? Z = invNorm(.90) = = x – = x – 1815 X = or 2138

Heights Example The heights of 18 to 24 year old males in the US are approximately normal with mean 70.1 inches and standard deviation 2.7 inches. The heights of 18 to 24 year old females have a mean of 64.8 inches and a standard deviation of 2.5 inches. How tall does a US woman between 18 and 24 have to be to be at the 35th percentile? – Z = invNorm(.35) = – = x – – = x – 64.8 – X = inches In order to be in the Tall Club of America, you must be in the top 10% height range. What is the cut off for males? For females? – Z = invNorm(.90) = = x – = x – = x – = x – 64.8 – x = inches x = 68 inches (6’ 1.5” for males) (5’8” for females)

Born to Run A study of elite distance runners found a mean body weight of pounds with a standard deviation of 10.6 pounds. How much would a runner weigh to be in the 75 th percentile? invNorm(.75) = = (x – 139.1)/10.6 X = pounds 40% of the runners weigh more than pounds. invNorm(.6) = = (x – 139.1)/10.6 X = pounds

Using z-scores in a Normal Distribution Find the percent: find the z-score using the formula then use the table or normalcdf to find the % Given the percent: find the z-score using the table or invNorm then solve for the observation using the z-score formula Z = observation – mean standard deviation

Reminders Z – score = standard score = # of standard deviations above or below the mean A z- score is NOT a percent!