6.4: Applications of the Standard Normal Distribution

Slides:

Advertisements

Similar presentations

Chapter 2: The Normal Distributions

Advertisements

The Normal Distribution

Chapter 2 Exploring Data with Graphs and Numerical Summaries

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

Normal Distributions: Finding Probabilities

Measures of Dispersion or Measures of Variability

2-5 : Normal Distribution

The Normal Models/Distributions. Normal Distribution Parameters The first parameter specified here is shape: symmetric, unimodal, bell shaped. (A formula.

The Normal Distribution

Applying the Standard Normal Distribution to Problems

Warm-up 2.5 The Normal Distribution Find the missing midpoint values, then find mean, median and standard deviation.

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

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.

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?

Sec 6.2 Bluman, Chapter Applications of the Normal Distributions The standard normal distribution curve can be used to solve a wide variety.

Interpreting Performance Data

Areas Under Any Normal Curve. EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that.

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

Density Curves Section 2.1. Strategy to explore data on a single variable Plot the data (histogram or stemplot) CUSS Calculate numerical summary to describe.

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.

MDM4U Chapter 3 Review Normal Distribution Mr. Lieff.

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

Numerical Measures of Variability

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

Compare the following heights in inches: BoysGirls

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.

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.

Section 5.2: PROBABILITY AND THE NORMAL DISTRIBUTION.

COMPUTATIONAL FORMULAS AND IQR’S. Compare the following heights in inches: BoysGirls

STATISTICS Chapter 2 and and 2.2: Review of Basic Statistics Topics covered today:  Mean, Median, Mode  5 number summary and box plot  Interquartile.

Describing Data Week 1 The W’s (Where do the Numbers come from?) Who: Who was measured? By Whom: Who did the measuring What: What was measured? Where:

Section 5.2 Normal Distributions: Finding Probabilities © 2012 Pearson Education, Inc. All rights reserved. 1 of 104.

Quiz 1. Find the area under the standard normal curve to the right of z = Find the area under the standard normal curve between z = and.

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

Let’s recap what we know how to do: We can use normalcdf to find the area under the normal curve between two z-scores. We proved the empirical rule this.

Measures of Central Tendency and Variation

Please copy your homework into your assignment book

Objectives Find probabilities for normally distributed variables

Assuming a normal distribution…

PROBABILITY AND STATISTICS

Using the Calculator for Normal Distributions

Describing Location in a Distribution

Random Variables and Probability Distribution (2)

Chapter 3: Normal R.V.

The Normal Distribution

STAT 206: Chapter 6 Normal Distribution.

3-3: Measures of Position

Other Normal Distributions

Ch. 18- Descriptive Statistics.

(12) students were asked their SAT Math scores:

QUIZ Time : 90 minutes.

Chapter 6: Random Variables

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.

How to Find Data Values (X) Given Specific Probabilities

Elementary Statistics: Picturing The World

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

Constructing Box Plots

Applications of the Normal Distribution

Measures of Central Tendency and Variation 8-1

Click the mouse button or press the Space Bar to display the answers.

Chapter 5 Normal Probability Distributions.

The Normal Curve Section 7.1 & 7.2.

Homework: pg. 142 #29, 30 pg. 147 # ) A B C D ) A B C D ) A B

Continuous Probability Distributions

Chapter 5 Normal Probability Distributions.

Homework: pg. 500 #41, 42, 47, )a. Mean is 31 seconds.

Chapter 5 Normal Probability Distributions.

Presentation transcript:

6.4: Applications of the Standard Normal Distribution By the end of class you will be able to solve real world problems using the normal distribution and determine if a distribution is normal.

The average admission charge for amusement parks is normally distributed with a mean of $45 and standard deviation of $6.50. Find the probability that an amusement park ticket is less than $40. .2209

Method 1: Convert to z value Use the formula to convert variable to z value Use normalCDF (low, high, z)

Method 2: No Conversion Use normCDF (low, high, mean, st. dev)

The winnings of Wheel of Fortune contestants are normally distributed with a mean of $16,000 and a standard deviation of $2,100

Calculate the following P(X<$15,000) P(X>$19,000) P($9,000<X<$24,500) 1) .1169, 2) 0, 3) .0764

The average length of a hospital stay is 5. 9 days The average length of a hospital stay is 5.9 days. If we assume a normal distribution and a standard deviation of 1.7 days, 15% of hospital stays are less than how many days? 4.13

Finding Variable Values Use invNORM( area to left, mean, st. dev)

The average person is willing to spend $6,000 on a used car The average person is willing to spend $6,000 on a used car. He wants to sell cars that appeal to the middle 70% of the population. The distribution is normally distributed with a standard deviation of $500. Find the minimum and maximum prices of a car that the dealer will sell. 5481, 6518

The following data represents the number of runs scored by a baseball player each year of his career. Check for normailty. 30 59 69 50 58 71 55 43 66 52 56 62 36 13 29 17 3 Create a frequency table and histogram with students, mean = 45.24, median = 52, s = 20.58, Q1 29.5, Q3 60.5, PI (-.985), Quartile Check: IQR = 31, Q1-1.5(IQR) = -17, Q3+1.5(IQR) = 107

Tests for Normality Construct a frequency distribution and histogram (bell curve) Use Pearson’s Index: (s = standard deviation) Check for outliers using IQR (Q1—1.5IQR, Q3+1.5IQR)

A survey of grocery stores showed how many days’ inventory the stores had. Check for normality. 5 29 34 44 45 63 68 74 74 81 88 91 97 98 113 118 151 158 See book pg 313. Have different rows do different tests.