# Sample Mean Probability | Statistics

"A recent study reported that average apartment rent in the U.S. is​ \$1,083. A random sample of 39 apartments was selected. Using a population standard deviation of​ \$227, what is the probability that the sample mean will be greater than​ \$1,035?" • What have you tried so far? What theorem do you know about that describes the distribution of a sample mean? – ConMan Nov 21 '16 at 0:23 ## 1 Answer Restatement and outline: You are given population mean$\mu = 1083$and population SD$\sigma = 227.$The mean$\bar X$of a sample of size$n = 39$has$E(\bar X) = \mu,\; SD(\bar X) = \sigma/\sqrt{n}$and$\bar X \sim Norm(\mu, \sigma/\sqrt{n})$. You seek$P(\bar X > 1035).$Now, standardize$\bar X\$ and use a standard normal table to evaluate this probability.

In problems like this, it is always a good idea to try to make a sketch to visualize the normal density curve and the relevant area. Here is a sketch.

Welcome to the site. Most of us expect to see some engagement with the problem on your part. Perhaps you can edit your computation and numerical answer into your Question to show you understand, to prevent down-votes or getting the Question closed, and maybe even get an up-vote.