The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 7 inches and an unknown population mean. If a random sample of 20 dogs is taken and results in a sample mean of 21 inches, find a 95% confidence interval for the population mean.

The 95% confidence interval for the population mean is between 17.93 inches and 24.07 inches.

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 21 - 3.07 = 17.93 inches.

The upper end of the interval is the sample mean added to M. So it is 21 + 3.07 = 24.07 inches

The 95% confidence interval for the population mean is between 17.93 inches and 24.07 inches.