The Normal Distribution Lake Maggiore, St. Petersburg, Florida.

Slides:

Advertisements

Similar presentations

Z-Scores are measurements of how far from the center (mean) a data value falls. Ex: A man who stands 71.5 inches tall is 1 standard deviation ABOVE the.

Advertisements

The Normal Distribution

Suppose Z ~ N(0, 1). Use the standard Normal table or your calculator to find P(z  -2.30)

Chapter 6 Normal Random Variable

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?

THE STANDARD NORMAL Unit 5, Day 3. Learning Goals for Today I can state the difference between a Normal Distribution and a Standard Normal Distribution.

The percent of calories from fat that a person in the United States consumes is normally distributed with a mean of about 36 and a standard deviation of.

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

Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,

Sampling distributions. Example Take random sample of 1 hour periods in an ER. Ask “how many patients arrived in that one hour period ?” Calculate statistic,

Section 3.4 Bootstrap Confidence Intervals using Percentiles.

Distribution of Sample Means, the Central Limit Theorem If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called.

Sampling Distributions

Precipitation Statistics! What are the chances?. Weather service collects precipitation data around the country.

Slide 4- 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Active Learning Lecture Slides For use with Classroom Response.

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.

Normal Distribution Problems

Ibrahim Altubasi, PT, PhD The University of Jordan

From Last week.

Sampling Distributions. Parameter A number that describes the population Symbols we will use for parameters include  - mean  – standard deviation.

Review from before Christmas Break. Sampling Distributions Properties of a sampling distribution of means:

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

American Alligator Ricky Pannell & Christopher Locke.

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.

Normal Distribution Real World Examples.

Ch. 2 – Modeling Distributions of Data Sec. 2.2 – Assessing Normality.

Chapter 7: Introduction to Sampling Distributions Section 2: The Central Limit Theorem.

Sampling Distribution WELCOME to INFERENTIAL STATISTICS.

3 common measures of dispersion or variability Range Range Variance Variance Standard Deviation Standard Deviation.

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

If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter,

7.2 Notes Central Limit Theorem. Theorem 7.1 – Let x be a normal distribution with mean μ and standard deviation σ. Let be a sample mean corresponding.

Chapter 9 Review Game. Question 1  On a scale of 1 to 10, ratings about school cafeteria food have a mean of 4.2 and a standard deviation of 1.6. If.

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

Chapter 7 The Normal Probability Distribution 7.3 Applications of the Normal Distribution.

Binomial Distributions Mean and Standard Deviation.

Math 3 Warm Up 4/23/12 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,

Inverse Normal Calculations. Consider a population of crabs where the length of a shell, X mm, is normally distributed with a mean of 70mm and a standard.

Finding values Given a Probability

STANDARDIZED VALUES: LESSON 21. HOW CAN YOU USE STANDARDIZED VALUES TO COMPARE VALUES FROM TWO DIFFERENT NORMAL DISTRIBUTIONS? STANDARDIZED VALUE TELLS.

An Example of {AND, OR, Given that} Using a Normal Distribution By Henry Mesa.

 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.

Empirical Rule 68% 95% 99.7% % RULE Empirical Rule—restated 68% of the data values fall within 1 standard deviation of the mean in either direction.

Properties of Normal Distributions 1- The entire family of normal distribution is differentiated by its mean µ and its standard deviation σ. 2- The highest.

Section 2 Standard Units and Areas under the Standard Normal Distribution.

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

From: Nuclear Power as a Basis for Future Electricity Generation

Standardized scores and the Normal Model

Normal Distribution.

Chapter 9.3: Sample Means Mr. Lynch AP Statistics.

Example of Poisson Distribution-Wars by Year

Other Normal Distributions

Warm Up A recent study found that 79% of U.S. teens from years old use Snapchat. Suppose samples of 100 U.S. teens from years old are taken.

Warm Up 1) A 2016 study from the State Department found that 46% of American citizens hold a passport. If repeated samples of 40 American citizens are.

An Example of {AND, OR, Given that} Using a Normal Distribution

Warm Up 1) A 2016 study from the State Department found that 46% of American citizens hold a passport. If repeated samples of 40 American citizens are.

Warm Up A recent study found that 79% of U.S. teens from years old use Snapchat. Suppose samples of 100 U.S. teens from years old are taken.

Use the graph of the given normal distribution to identify μ and σ.

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.

10-5 The normal distribution

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

Basic concepts in probability

Warm Up What ocean was to the east of China?

Normal Distributions.

Random Variables and Probability Distributions

Sample Means and Proportions Scavenger Hunt Review

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.

Consider the following problem

Presentation transcript:

The Normal Distribution Lake Maggiore, St. Petersburg, Florida

Alligators are only native to the United States and China. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet and an approximately normal distribution. What proportion of adult males are less than 9 feet? ̶ 1.07 P(x < 9) =.1428

The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. The largest alligator recorded in Florida was 17.4 feet. What is the probability an adult male alligator is more than 17 feet? 2.82 P(x > 17) =.0024

The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. What is the probability an adult male alligator is between 12 and 14 feet long?.39 P(12 < x < 14) =

The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. What is the cut off length for the largest 15% of American alligators? x = feet x

In China, the alligator is extremely endangered and can only be found along the Yangtze River. The average length of the Chinese alligator is 5 feet with a standard deviation of Chinese legend says that the largest Chinese alligator was measured to be 10 feet long. The largest alligator recorded in the U.S. was an alligator from Louisiana that measured 19 feet 2 inches. N(11.2, 2.06)

In China, the alligator is extremely endangered and can only be found along the Yangtze River. The average length of the Chinese alligator is 5 feet with a standard deviation of Chinese legend says that the largest Chinese alligator was measured to be 10 feet long. The largest alligator recorded in the U.S. was an alligator from Louisiana that measured 19 feet 2 inches. N(11.2, 2.06) Which alligator measures to be in the highest percentile for their country?

Chinese: 10 feet N(5,.67) American: 19 feet 2 inches N(11.2, 2.06) Which alligator measures to be in the highest percentile for their country?

END