VCU STAT 210  Lecture21 (76 pages)
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Lecture21
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 76
 School:
 Virginia Commonwealth University
 Course:
 Stat 210  Basic Practice of Statistics
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STAT 210 Lecture 21 Normal Distributions October 13 2017 Test 4 Wednesday October 18 Covers chapter VI pages 139 168 Combination of short answer questions and problems Formulas and normal table provided please bring calculator and writing instrument Practice Problems Pages 162 through 165 Relevant problems VI 6 through VI 15 Recommended problems VI 14 and VI 15 Additional Reading and Examples Read pages 158 through 160 TOP HAT 2 Notation X N m s X is distributed normal with mean m and standard deviation s Standard Normal Distribution Denoted by Z Has population mean m 0 center Has population standard deviation s 1 spread Shape is normal symmetric bell curve No unusual features Z N 0 1 Probabilities are tabled on pages 338 339 Probability The normal table gives the probability that the standard normal variable Z falls below some specified value z less than problems Read the value of z down the left most column and across the top row and read the probability from the body of the table Probability Suppose X is distributed normal with some mean m not equal to 0 and or some standard deviation s not equal to 1 X N m s Z Score Transformation We convert to a standard normal variable Z N 0 1 Z X m value mean s standard deviation Z Score Transformation P a X b P a m X m b m s P a m s s s Z b m s Once converted from X to Z the standard normal table on pages 338 and 339 is used to find the probability just as in Examples 34 through 41 Probability Problems on Calculator 1 Hit 2nd then VARS this gives a list of distributions 2 Choose option 2 normalcdf 3 Enter four numbers the lower number of the interval the upper number of the interval the mean and the standard deviation Standard Normal Distribution All of the problems so far asked us to find the probability given a value or values of Z Now suppose the probability or area or proportion or percentage is given and we want to find the corresponding value of Z see page 145 There are three such problems Less Than Problem Suppose you want to find the value z such that the probability of being less than z or less than and equal to z is as specified To solve 1 Draw a normal curve and mark the information stated in the problem 2 In the normal table find the specified less than probability in the body of the table and then read across and up to determine the appropriate z value Value Problems on the Calculator See pages 160 and 161 for instructions for using the calculator to determine normal probabilities and values of normal variables 1 Hit 2nd then VARS this gives a list of distributions 2 Choose option 3 invNorm 3 You must enter three numbers the LESS THAN probability then the mean which is currently
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