For the total population of a large southern city, mean family income is $34,000, with a standard deviation (for the population) of $5,000. imagine that your are taking a subsample of 200 city residents. what is the probability that the sample mean exceeds $37,000?

Less than .0001

Step-by-step explanation:

The population and sample mean  family income are the same: $34,000.

The sample standard deviation is given by:

For any give income, X, the correspondent z-score of the distribution is given by:

For X = $37,000:

Traditional z-score tables present values up to 3.49 at the 99.98-th percentile. A z-score of 8.485, which is way above the upper represented limit, denotes an almost zero probability that the sample mean exceeds $37,000.

It is fair to say that the probability that the sample mean exceeds $37,000 is less than .0001