The number of square feet per house is normally distributed with a population standard deviation of 154 square feet and an unknown population mean. If a random sample of 16 houses is taken and results in a sample mean of 1550 square feet, find a 80% confidence interval for the population mean. Round your answer to TWO decimal places. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above.

The 80% confidence interval for the population mean is between 1500 square feet and 1600 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 1550 - 50 = 1500 square feet.

The upper end of the interval is the sample mean added to M. So it is 6.4 + 1550 + 50 = 1600 square feet.

The 80% confidence interval for the population mean is between 1500 square feet and 1600 square feet.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)