Credit Union Incomes. Find the 90% confidence interval of the population mean for the incomes of Pennsylvania credit unions. A random sample of 50 credit unions is shown. The data are in thousands of dollars.

Solution: We have the following table:

The population standard deviation is not known, but the sample size is large enough to apply a normal approximation usingas an approximation of. Therefore, we get that the interval is approximated as

wherecorresponds to the two-tailed z-critical value for. Hence, we get

This means that there is a probability of that the actual population mean is contained by the interval.