Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85. (Round your answers to two decimal places.)

The 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85 is between 4.54 and 5.16.

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 the margin of error 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 4.85 - 0.31 = 4.54.

The upper end of the interval is the sample mean added to M. So it is 5.85 + 0.31 = 5.16.

The 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85 is between 4.54 and 5.16.