Download presentation

1
Z scores MM3D3

2
**Recall: Empirical Rule**

68% of the data is within one standard deviation of the mean 95% of the data is within two standard deviations of the mean 99.7% of the data is within three standard deviations of the mean 99.7% 95% 68% 𝑥 −3𝑠 𝑥 −2𝑠 𝑥 −𝑠 𝑥 𝑥 +𝑠 𝑥 +2𝑠 𝑥 +3𝑠

3
**Example IQ Scores are Normally Distributed with N(110, 25)**

Complete the axis for the curve 99.7% 95% 68% 35 60 85 110 135 160 185

4
**Example What percent of the population scores lower than 85? 16% 99.7%**

95% 68% 35 60 85 110 135 160 185

5
**Example What percent of the population scores lower than 100? 99.7%**

95% 68% 35 60 85 100 110 135 160 185

6
Z Scores Allow you to get percentages that don’t fall on the boundaries for the empirical rule Convert observations (x’s) into standardized scores (z’s) using the formula: 𝑧= 𝑥−𝜇 𝜎

7
**Practice: Convert the following IQ Score N(110, 25) to z scores:**

100 125 75 140 45 -.4 .6 -1.4 1.2 -2.6

8
Z Scores The z score tells you how many standard deviations the x value is from the mean The axis for the Standard Normal Curve: -3 -2 -1 1 2 3

9
Z Score Table: The table will tell you the proportion of the population that falls BELOW a given z-score. The left column gives the ones and tenths place The top row gives the hundredths place What percent of the population is below .56? .7123 or 71.23%

10
Z Score Table: The table will tell you the proportion of the population that falls BELOW a given z-score. The left column gives the ones and tenths place The top row gives the hundredths place What percent of the population is below .4? .6554 or 65.54%

11
Practice: Use your z score table to find the percent of the population that fall below the following z scores: z < 2.01 z < 3.39 z < 0.08 z < -1.53 z < -3.47 97.78% 99.97% 53.19% 6.30% .03%

12
Using the z score table You can also find the proportion that is above a z score Subtract the table value from 1 or 100% Find the percent of the population that is above a z score of 2.59 z > 2.59 .0048 or .48% Find the percent of the population that is above a z score of -1.91 z > -1.91 .9719 or 97.19%

13
Using the z score table You can also find the proportion that is between two z scores Subtract the table values from each other Find the percent of the population that is between .27 and 1.34 .27 < z < 1.34 .3035 or 30.35% Find the percent of the population that is between and 1.89 -2.01 < z < 1.89 .9484 or 94.84%

14
Practice worksheet

15
**Application 1 IQ Scores are Normally Distributed with N(110, 25)**

What percent of the population scores below 100? Convert the x value to a z score 𝑧= 𝑥−𝜇 𝜎 z < -.4 Use the z score table .3446 or 34.46% = 100−110 25 =−.4

16
**Application 2 IQ Scores are Normally Distributed with N(110, 25)**

What percent of the population scores above 115? Convert the x value to a z score 𝑧= 𝑥−𝜇 𝜎 z > .2 Use the z score table .5793 fall below .4207 or 42.07% = 115−110 25 =.2

17
**Application 3 IQ Scores are Normally Distributed with N(110, 25)**

What percent of the population score between 50 and 150? Convert the x values to z scores 𝑧= 𝑥−𝜇 𝜎 -2.4 < z < 1.6 Use the z score table .9452 and .0082 This question is asking for between, so you have to subtract from each other. .9370 or 93.7% = 150−110 25 =1.6 = 50−110 25 =−2.4

18
Practice worksheet

Similar presentations

Presentation is loading. Please wait....

OK

Resistência dos Materiais, 5ª ed.

Resistência dos Materiais, 5ª ed.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download maths ppt on circles for class 9 Ppt on mobile phones operating systems Ppt on computer graphics applications Ppt on chapter 3 atoms and molecules Ppt on varactor diode testing Ppt on blood stain pattern analysis jobs Ppt on mars one astronauts Ppt on seven segment display circuit Ppt on group decision making techniques Ppt on sea level rise due