Question 1185733
the population mean is 173
the population standard deviation is 55
the sample size is 173


the standard error is equal to the standard deviation divided by the square root of the sample size = 55/sqrt(173) = 4.181572567.


round to two decimal places to get a standard error of 4.18.


the standard error is the standard deviation of the distribution of sample means.


the mean of each sample taken will be within a certain range depending on the confidence interval.


if you take enough samples, the mean of all the samples will approach the mean of the population.


the larger the sample size, the closer to the population mean will the sample mean be.


as an example, assume the confidence interval is .99.
that means that 99% of the samples will have a mean that is within the confidence interval.


your population mean is 173.
your population standard deviation is 55


with a sample size of 173, the standard error is 55 / sqrt(173) = 4.18157.


99% of your sample means will be between 162.229 and 183.771


<img src = "http://theo.x10hosting.com/2021/100702.jpg" >


with a sample size of 1000, the standard error is 55 / sqrt(1000) = 1.73925.


99% of your sample means will be between 168.52 and 177.48.


<img src = "http://theo.x10hosting.com/2021/100703.jpg" >


with a sample size of 10,000, the standard error is 55 / sqrt(10000) = .55


99% of your sample means will be between 171.583 and 174.417


<img src = "http://theo.x10hosting.com/2021/100704.jpg" >


the spread of the sample means get less the larger the size of each sample.


i think the simple answer will be that the distribution of sample means will have a mean of 173 and a standard error of 4.18


hopefully, that's what you're looking for.