Upon reaching orbit the Space Shuttle will engage in MECO (Main Engine Cut-Off). At that time it will be traveling at an average of 17,580mph (σ = 35mph).

Slides:

Advertisements

Similar presentations

5.1 Normal Probability Distributions Normal distribution A continuous probability distribution for a continuous random variable, x. The most important.

Advertisements

Chapter – 5.4: The Normal Model

CHAPTER 6: The Standard Deviation as a Ruler & The Normal Model

A Day of Classy Review.

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?

Normal Distribution Calculations

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

z-Scores What is a z-Score? How Are z-Scores Useful? Distributions of z-Scores Standard Normal Curve.

Chapter 6 Normal Probability Distributions

Copyright © Cengage Learning. All rights reserved. 6 Normal Probability Distributions.

Warm-up 2.5 Day 2 1)An incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 82 and in math, 86. The.

Lesson Normal Distributions.

Warm-Up The probability that a person owns and I-phone is  What is the probability that in a random group of 10 people, at least 7 own an I-phone?

Using the Empirical Rule. Normal Distributions These are special density curves. They have the same overall shape  Symmetric  Single-Peaked  Bell-Shaped.

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.

Z-Scores Z-Score: It is a measure of a the position specific value in a data set relative to mean in terms of the standard deviation units. It is sometimes.

2.5 Normal Distribution SWBAT calculate areas under a standard normal curve in writing by converting between values and z- scores using a GCD or Table.

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

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.

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.

Review Ways to “see” data –Simple frequency distribution –Group frequency distribution –Histogram –Stem-and-Leaf Display –Describing distributions –Box-Plot.

7.2 The Standard Normal Distribution. Standard Normal The standard normal curve is the one with mean μ = 0 and standard deviation σ = 1 We have related.

Standard Normal Distribution.  P ,33,34,35.

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.

The Normal Distribution. The Area under the curve The area under the curve represents everything: 100%.

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

Chapter 7: The Normal Distribution. Important Properties of a Normal Distribution The mean, median, and mode have the same value, which is located exactly.

Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 9 Statistics.

Chapter 2 Modeling Distributions of Data Objectives SWBAT: 1)Find and interpret the percentile of an individual value within a distribution of data. 2)Find.

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

2.2 Standard Normal Calculations

Chapter 6 The Normal Distribution.  The Normal Distribution  The Standard Normal Distribution  Applications of Normal Distributions  Sampling Distributions.

Chapter 2 – Day 1.

AP Statistics: Section 2.2 B. Recall finding a z-score in section 2.1: z =

Educational Research: Competencies for Analysis and Application, 9 th edition. Gay, Mills, & Airasian © 2009 Pearson Education, Inc. All rights reserved.

7.4 Use Normal Distributions p Warm-Up From Page 261 (Homework.) You must show all of your work for credit 1.) #9 2.) #11.

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

Section 6-1 Overview. Chapter focus is on: Continuous random variables Normal distributions Overview Figure 6-1 Formula 6-1 f(x) =  2  x-x-  )2)2.

Normal Distribution S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Normal Distribution SOL: AII Objectives The student will be able to:  identify properties of normal distribution  apply mean, standard deviation,

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,

1 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Chapter 5 The Standard Deviation as a Ruler and the Normal Model.

Normal Distribution. Normal Distribution Curve A normal distribution curve is symmetrical, bell-shaped curve defined by the mean and standard deviation.

Normal Distribution SOL: AII Objectives The student will be able to:  identify properties of normal distribution  apply mean, standard deviation,

Characteristics of Normal Distribution symmetric with respect to the mean mean = median = mode 100% of the data fits under the curve.

THE NORMAL DISTRIBUTIONS Chapter 2. Z-Scores and Density Curves.

Up to now, our discussion of the normal distribution has been theoretical. We know how to find the area under the normal bell curve using the normalcdf.

Discrete Math Section 17.4 Recognize various types of distributions. Apply normal distribution properties. A normal distribution is a bell shaped curve.

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

Normal Distribution SOL: AII

Applications of Normal Distributions

Describing Location in a Distribution

Top, Middle, & Bottom Cutoff Scores……

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.

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.

Other Normal Distributions

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

WARM – UP Jake receives an 88% on a Math test which had a N(81, 8). That same day he takes an English test N(81, 12) and receives a 90%. Which test did.

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.

Normal Distributions, Empirical Rule and Standard Normal Distribution

Normal Distribution SOL: AII

CHAPTS 3 & 5 Z Score, and Basic Concepts of Probability

Normal Distribution SOL: AII

Normal Distribution with Graphing Calculator

Normal Distribution.

Objectives The student will be able to:

Normal Distribution SOL: AII

Presentation transcript:

Upon reaching orbit the Space Shuttle will engage in MECO (Main Engine Cut-Off). At that time it will be traveling at an average of 17,580mph (σ = 35mph). A speed between and is needed to keep the Shuttle in orbit. Below is too slow.a.) What proportion of Shuttles reach this target interval? b.) What proportion of Shuttles have to fire secondary engines to correct speed because they are going to slow? c.) The top 1% of Shuttles accelerate over what speed? P(17500 < x < 17660) = Normalcdf(-2.286, 2.286) a.) b.) c.) mph P(x < 17500) = Normalcdf(-E99, ) InvNorm(.99) = = (X – 17580)/35

WARM – UP P(x<#) Jake receives an 88% on a Math test which had a N(81, 8). That same day he takes an English test N(81, 12) and receives a 90%. Which test did he do better on with respect to the rest of the class? Support your answer by converting each score into a z-score and then calculating the percent of students he did better than for each test (percentile = P(x<#). Math: P(x < 88) = English: P(x < 90) = P(z < 0.875) = Normalcdf(-E99, 0.875) Jake did better than 80.9% of his peers. P(z < 0.75) = Normalcdf(-E99, 0.75) Jake did better than 77.3% of his peers.

Normal Proportion Calculations ●State the Problems as an Inequality: P(x #) or P(a < x < b) ●Draw a picture if necessary. ●Standardize the value by using the z-score formula. ●Use the Calculator [normalcdf (lower, upper)] to find the proportion. ●Draw a picture if necessary. ●Find the Standardized value (z) by using [InvNorm(.%)]. (% to the LEFT) ●Solve for the x within the z-score formula. Finding Values from Proportions

1.A recent Statistics Test produced a. What proportion of the class scored below a 75 on the test? P( x < 75 ) = P(z < ) normalcdf(-E99, ) = First, Convert 75 to a z-score Normcdf = Proportion or % InvNorm = z-score

2. A recent Statistics Test produced a. What score did a statistics student need to have earned in order to be within the Top 10% of the class? Hint: a) First find the z-score for the 90 th Percentile. b) Within the z-score formula substitute the z, the μ, the σ, and then solve for x. X = 93.7 = 94% InvNorm(.90) = % 90%

3.Between what scores does a student have to get to be in the Middle 50% of the class? < X < InvNorm(.25) = Q1Q1 Q3Q3 InvNorm(.75) = %

4. The ACT exam scores follow a normal distribution. If the top 10% scored above a 34 and the bottom 20% scored below a 18, what is the mean and standard deviation? Hint: a) First find the z-score for the 90 th Percentile. Then find the z-score for the 20 th Percentile b) Within two z-score formulas substitute the z and x and then solve for the μ and the σ. InvNorm(.90) = InvNorm(.20) =

Application A headache medicine is effective if it demonstrates relief (a score of 5 or higher) for over 75% of the population. If patients are asked to describe the effects of a new drug by rating it on a scale from 1(NO Effect) to 10(Complete Relief), and their responses follow a N (5.8, 1.3): 1. What Proportion of the population indicated a relief score of 3 or below? 2. What score represents the top 75% of the population? 3. What Proportion of the population indicate a relief score 5 or higher? X: Z: % %

1.If the GPA of seniors follows, what proportion of the senior class has a GPA below 3.0? P( x < 3.0 ) = P(z < ) normalcdf(-E99, ) =

2. If the GPA of seniors follows, what GPA would represent the top 5% of the senior class? X = InvNorm(.95) = % Hint: a) First find the z-score for the 95 th Percentile. b) Within the z-score formula substitute the z 95, the μ, and the σ, and then solve for x

Between what GPA’s does a student have to get to be in the Middle 50% of the senior class if the distribution is ? < X < InvNorm(.25) = Q1Q1 Q3Q3 50% 25%25% InvNorm(.75) = IQR = Q 3 – Q 1

You are interested in finding the proportions of high school students who travel various miles for college. An approximately normal distribution of students reveal a N(210, 88). 1) What proportion traveled more than 300 miles? 2) What proportion traveled more than 450 miles? 3) What proportion traveled less than 100 miles? 4) What distance, in miles, represents the 90 th Percentile? 5) What distance, in miles, do the top 5% represent? 6) What percent of students stay close to home by traveling within 5 to 60 miles? miles 355 miles 3.42% P(x > 300) = P(z > ) Normalcdf(1.0227, E99) P(x > 450) = P(z > ) Normalcdf(2.7273, E99) P(x < 100) = P(z < -1.25) Normalcdf(-E99, -1.25) InvNorm(.90) z = = (X – 210)/88 InvNorm(.95) z = = (X – 210)/88 P(5 < x < 60) = P( < z < ) Normalcdf( , )