A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 10.2 reproductions and the population standard deviation is known to be 2.4. If a sample of 907 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the virus. Round your answers to one decimal place

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.

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 10.2 - 0.1 = 10.1 reproductions per hour.

The upper end of the interval is the sample mean added to M. So it is 10.2 + 0.1 = 10.3 reproductions per hour.

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.