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How many adults must be randomly selected to estimate the mean FICO score of working...

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surfer3 | Valedictorian

Posted June 1, 2012 at 1:40 AM via web

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How many adults must be randomly selected to estimate the mean FICO score of working adults in the United States given the following information

The sample mean should lie within 3 points of the population mean with a 95% confidence interval and the population standard deviation is 68.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 2, 2012 at 1:25 PM (Answer #1)

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The population standard deviation is 68. The number of people that need to form part a sample if the sample mean should lie within 3 points of the population mean with a 95% confidence interval has to be determined.

Using the central limit theorem approximately 95% of the sample means will fall within 1.96 standard errors of the population mean.

`1.96*(sigma/sqrt n) = 3`

As `sigma = 68`

`1.96*(68/sqrt n) = 3`

=> `sqrt n = (1.96*68)/3`

`n ~~ 1974`

The number of adults that must be randomly selected to estimate the mean FICO score is approximately 1974.

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