# How many adults must be randomly selected to estimate the mean FICO score of working adults in the United States given the following informationThe sample mean should lie within 3 points of the...

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.

justaguide | Certified Educator

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.