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Unformatted text preview: & 6.13. a. The population from which we are randomly sampling n = 35 measurements is not necessarily normally distributed. However, the sampling distribution of x does have an approximately normal distribution, with mean and standard deviation n / . The probability of interest is [ ] [ ] [ ] [ ] 1 ) ( 1 ) ( 1 ) ( 1 1- <-- <- = <- <- = <- x P x P x P x P Standardizing, we have: [ ] [ ] [ ] [ ] & - +- <- & - + < = +- <- + < =- <-- <- 35 / 12 ) 1 ( 35 / 12 ) 1 ( 1 1 1 ) ( 1 ) ( z P z P x P x P x P x P [ ] [ ] 3758 . ) 1879 . ( 2 493 . 493 . = =- <- < = z P z P where, since is unknown, we use the sample standard deviation s = 12 (we can do this, since the sample size is large enough). b. No. There are many possible values for x , the actual percent tax savings, as given by the probability distribution for x . 6.16. a. The sample mean x is normally distributed, since the original strength measurements are Normally distributed, with mean and standard deviation...
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.
- Spring '08