# sample mean

#### jessi

##### New Member
The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and standard deviation equal to$2,490. Based on this, if a sample of size n=36 is selected the highest sample mean that we would expect to see would be approximately \$38,034.

My teacher said this is true, but how do I get this answer?

#### JohnM

##### TS Contributor
Hint:

The sample means will have:

1. a normal distribution with a mean equal to the population mean, and
2. a standard error equal to the population standard deviation divided by the square root of the sample size

Use the z-tables to figure out if 38,034 is about as high as you might expect the sample mean to get, if you took many, many samples of size 36 (probably around 3 standard errors above the sample mean....)