VCU STAT 210  Lecture22 (30 pages)
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Lecture22
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 30
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 Virginia Commonwealth University
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 Stat 210  Basic Practice of Statistics
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STAT 210 Lecture 22 t Distributions and Sampling Distributions October 16 2017 Test 4 Wednesday October 18 Covers chapter VI pages 139 168 Combination of multiple choice short answer questions and problems Formulas and tables provided please bring calculator and writing instrument Practice Problems Pages 162 through 165 Relevant problems VI 16 and VI 17 Recommended problems VI 16 and VI 17 Additional Reading and Examples Read pages 158 through 160 TOP HAT 2 Motivating Example The population consists of a group of people in an investment club and the variable of interest is X the age of each person in the investment club Suppose that the ages of people in the investment club follow an approximate normal distribution with mean 41 years and standard deviation 11 years Then X N 41 11 Motivating Example Problems X N 41 11 1 Find the probability that an investor s age is less than 19 P X 19 2 Find the probability that an investor s age is greater than 57 P X 57 3 What must an investor s age be such that the probability of being less than that age is 1685 Motivating Example Answers X N 41 11 1 P X 19 P Z 19 41 P Z 2 00 0228 11 Calculator normalcdf 1E99 19 41 11 2 P X 57 P Z 57 41 P Z 1 45 11 1 P Z 1 45 1 9265 0735 Calculator normalcdf 57 1E99 41 11 Motivating Examples Answers X N 41 11 3 Find x such that P X x 1685 Find p 1685 in the body of the table read across and up to find z 0 96 x m zs 41 0 96 11 41 10 56 30 44 Calculator invNorm 1685 41 11 Practice Problems Suppose X N 450 85 1 Find the probability that X is greater than 500 P X 500 2 Find the probability that X is between 400 and 640 P 400 X 640 Practice Problem Answers Suppose X N 450 85 1 Find the probability that X is greater than 500 P X 500 P Z 500 450 85 P Z 0 59 1 P Z 0 59 1 7224 2776 Calculator normalcdf 500 1E99 450 85 2 Find the probability that X is between 400 and 640 P 400 X 640 P 400 450 85 Z 640 450 85 P 0 59 Z 2 24 P Z 2 24 P Z 0 59 9875 2776 7099 Calculator normalcdf 400 640 450 85 t Distributions The past three lectures we have discussed the normal distributions To specify the normal distribution being used one must specify the values of the population mean m and the population standard deviation s In many cases the value of the population standard deviation s is not known and hence it is not possible to use the normal distributions In these cases the tdistributions are often used instead of the standard normal Z distribution t Distributions If
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