The number of square feet per house are normally distributed with a population standard deviation of 197 square feet and an unknown population mean. If a random sample of 25 houses is taken and results in a sample mean of 1820 square feet, find a 99% confidence interval for the population mean.

The 99% confidence interval for the population mean is betwen 1718.55 square feet and 1921.45 square feet.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1820 - 101.45 = 1718.55 square feet

The upper end of the interval is the sample mean added to M. So it is 1820 + 101.45 = 1921.45 square feet.

The 99% confidence interval for the population mean is betwen 1718.55 square feet and 1921.45 square feet.