Download presentation

Presentation is loading. Please wait.

Published byGrant Marsh Modified over 2 years ago

1
1 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 5-4 Normal Distributions: Finding Values

2
2 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 1. Don’t confuse z scores and areas. Z scores are distances away from the mean along the horizontal scale, but areas are regions under the normal curve. 2. Use invNorm() to find a z-score for a given percentage to the left(percentile). 3. A z score must be negative whenever it is located to the left of the centerline of 0. Cautions to keep in mind

3
3 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 0 0.95 1.64 95% z = invNorm(.95) Finding z Scores when Given Probabilities FIGURE 5-11 Finding the 95th Percentile ( z score will be positive)

4
4 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 0 0.80 -.84 0.20 80% Finding the top 80% Bottom 20% 20% Finding z Scores when Given Probabilities ( z score will be negative) z = invNorm(.20)

5
5 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Procedure for Finding Values (x) 1. Sketch a normal distribution curve, enter the given probability or percentage in the appropriate region of the graph, and identify the x value(s) being sought. 2.Use invNorm() to find the z score corresponding to the region bounded by x. Cautions: You must input the percentile (area below) into invNorm() If the area(%) is above you must enter its complement into invNorm() If the area(%) is the middle you must enter area(%) in the tail into invNorm(). You will have two opposite z-scores to define the interval. 3. Enter the values for µ, , and the z score found in step 2, then solve for x. x = µ + (z ) (z-score formula solved for x) 4. Refer to the sketch of the curve to verify that the solution makes sense in the context of the graph and the context of the problem.

6
6 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman What weight denotes the 10 th percentile of women’s weight? Assume women’s weights are normally distributed with a mean of 143 pounds and standard deviation of 29 pounds. Example

7
7 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143.10 x = ? 10% Finding P 10 for Weights of Women FIGURE 5-17 Weight

8
8 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143x = ? 0.10 Finding P 10 for Weights of Women 0 -1.28 Weight z = invNorm(.10) = -1.28 z

9
9 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143x = ? 0.10 Finding P 10 for Weights of Women 0 -1.28 x = + (z ) x = 143 + (-1.28 29) = 105.88 Weight

10
10 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143x = 106 0.10 Finding P 10 for Weights of Women FIGURE 5-17 0 -1.28 The weight of 106 lb (rounded) separates the lowest 10% from the highest 90%. Weight

11
11 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143x = 180 0.10 Forgot to make z score negative??? 0 1.28 x = 143 + (1.28 29) = 180 Weight

12
12 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 143x = 180 0.10 Forgot to make z score negative??? 0 1.28 UNREASONABLE ANSWER! Weight

13
13 Chapter 5. Section 5-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman xz% normalcdf(z left, z right ) invNormal(% to Left) x = +z

Similar presentations

Presentation is loading. Please wait....

OK

Estimating a Population Variance

Estimating a Population Variance

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Training ppt on etiquette and manners Ppt on electricity for class 10 download Download ppt on acids bases and salts class 10 Org chart download ppt on pollution Ppt on aircraft landing gear system ppt Ppt on travel and tourism industry in india Ppt on water pollution problems and solutions Ppt on environmental degradation vs industrial revolution Ppt on 9 11 attack on world trade center and effects Cerebellum anatomy and physiology ppt on cells