[PDF] Using The TI-83/84 Plus Chapter 6: Normal Distributions





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Using The TI-83/84 Plus Chapter 6: Normal Distributions

Using The TI-83/84 Plus Probabilities with the normalcdf Function ... Percentiles from a Normal Distribution with the invNorm Function.



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Using The TI-83/84 Plus

Chapter 6: Normal Distributions

The following pages give detailed instructions and links to instructional videos for the two main tasks found

in Chapter 6. Each topic has its own page or you can go directly to the videos.

Probabilities with thenormalcdfFunction2

For example, ifIQ'sare normally distributed with a mean of 100 and a standard deviation of 15, what

percentage of people have anIQbetween 110 and 125?Play Video.Percentiles from a Normal Distribution with theinvNormFunction3

For example, ifIQ'sare normally distributed with a mean of 100 and a standard deviation of 15, what IQseparates the top 10% from the rest? That is, ndP90.Play Video. 2 Finding Probabilities with thenormalcdfFunctionPlay Video.Getting to thenormalcdffunction 1. Hit 2 ndbutton then theVARSbutton to access theDISTR(distributions) menu. 2. Hig hlightthe DISTRoption and scroll down (using the down arrow#button) to highlight the normalcdfoption then hitENTER. The screen then shows normalcdf( and you can put in the variables from here. Usage for any normal distribution with meanand standard deviation Ifxis a normally distributed random variable, with mean =and standard deviation =, then

P(xmin< x < xmax) =normalcdf(xmin, xmax,,)

P(x < xmax)normalcdf(very low x-value, xmax,,)

P(x > xmin)normalcdf(xmin, very high x-value,,)

Examples:

SupposeIQ's are normally distributed with a mean of 100 and a standard deviation of 15. 1. Wha tp ercentageof p eopleha vean IQbetween 110 and 125? normalcdf(110;125;100;15) =0.2047or about 20% 2. Wha tp ercentageof p eopleha vean IQless than 125? normalcdf(1000;125;100;15) =.9522or about 95% 3. Wha tp ercentageof p eopleha vean IQgreater than 110? normalcdf(110;1000;100;15) =.2525or about 25% Usage for the standard normal (z) distribution (= 0and= 1). In the text we rst convertxscores tozscores using the formulaz= (x)=and then nd probabilities from thez-table. These probabilities can be found with thenormalcdffunction as well. The usage is the same, just be sure to set= 0 and= 1.

P(zmin< z < zmax) =normalcdf(zmin, zmax,0,1)

P(z < zmax)normalcdf(-100, zmax,0,1)

P(z > zmin)normalcdf(zmin, 100,0,1)

3 Finding percentiles from a Normal Distribution with theinvNormFunction .Play Video.Getting to theinvNormfunction 1. Hit 2 ndbutton then theVARSbutton to access theDISTR(distributions) menu. 2. Hig hlightthe DISTRoption and scroll down (using the down arrow#button) to highlight the invNormoption then hitENTER. The screen then shows invNorm( and you can put in the variables from here. Usage for any normal distribution with meanand standard deviation Suppose you want to nd thex-value that separates the bottomk% of the values from a distribution with meanand standard deviation. We denote this value in the text asPk. P k=invNorm(k (in decimal form),,) P

25=invNorm(0.25,,)

P

90=invNorm(0.90,,)

Examples:

SupposeIQ's are normally distributed with a mean of 100 and a standard deviation of 15. 1. Wh atIQseparates the lower 25% from the others? (FindP25.) P

25=invNorm(:25;100;15) =89.88

2. Wh atIQseparates the top 10% from the others? (FindP90.) P

90=invNorm(:9;100;15) =119.22

Usage for the standard normal (z) distribution (= 0and= 1). In the text we found thez-scores for a given percentile from thez-table and then converted these to x-values using the formulax=+z . These percentiles can be found with thenormInvfunction as well. The usage is the same, just be sure to set= 0 and= 1. P k=invNorm(k (in decimal form), 0, 1) P

25=invNorm(0.25, 0, 1) = -0.67449!-0.67

P

90=invNorm(0.90, 0, 1) = 1.28155!1.28

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